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Confetti rained down at the Nasdaq as Etsy Inc. ’s stock popped 94% in early trading. But all its CEO Chad Dickerson felt was dread.

His toddler had vomited and was throwing a tantrum. Mr. Dickerson, too, felt sick to his stomach as he worried about how the online crafts marketplace would live up to the hype. Back in the office, employees celebrated by dousing him with a bucket of ice water. He recalls the chill he felt the rest of the day in a cold, wet suit.

It was “this moment of success and this feverish insanity,” says the now-47-year-old Mr. Dickerson, who left as Etsy’s chief executive in 2017, two years after the initial public offering. Amid the confetti, he thought: “If we don’t maintain this price…it’s just going to be brutal.”

This year is set to be a huge one for startup IPOs. Going public is a cinematic moment for founders, CEOs and early employees, one that can turn years of hard work into immense wealth. But off-camera, the startup world has a dark side. Under the veneer of fancy parties and multibillion-dollar valuations, many founders and early-startup executives are striving to build pioneering businesses while wrestling with issues like anxiety, drug addiction, insomnia, depression and binge eating.

Stress, of course, is a part of any leadership role, and startup leaders often have more resources than most to cope with mental-health woes. But it is also becoming clear that the swashbuckling creativity that pushes many startup founders to take bold leaps often comes with inner demons.

Entrepreneurs were 50% more likely to report having a lifetime mental-health condition and reported significantly higher rates of depression, attention-deficit disorder, substance abuse and bipolar disorder than a control group, according to a 2016 paper by researchers at the University of California San Francisco, UC Berkeley, and Stanford University, who surveyed more than 200 founders.

Some entrepreneurs have “a high degree of energy, a low need for sleep, a drive that seems far beyond ordinary driven people and a vivid imagination,” says Kerry Sulkowicz, a New York psychoanalyst who advises CEOs. These traits allow them to “keep going when everybody tells you what you’re doing is crazy” but also makes them vulnerable to mental-health issues, he says.

A massive workload doesn’t help—nor that young entrepreneurs are bombarded by what some call “hustle porn,” the notion that working nonstop is a badge of honor.

Serial entrepreneur Kwiri Yang, 31, says she found herself in a “stress cage” as head of strategy at Fuhu, a children’s tablet maker. After Fuhu was sold to Mattel Inc. in a bankruptcy auction in 2016, she says she fell physically ill and grew severely depressed, cycling through seven therapists and three executive coaches before finding support from other founders.

Even established internet entrepreneurs say they aren’t immune to the crushing pressures.

“All the way through every fundraise, until you find your lead investor, you feel like crap because every other investor you talk to is telling you how much your business sucks,” said Kimbal Musk, 46, who says he fell into a depression after selling his and his brother Elon’s startup Zip2 for $307 million, making more money than he’d ever dreamed of at age 27.

Feeling lost, he enrolled in cooking school and went on to found food startups Kitchen Restaurant Group, Big Green and Square Roots.

Rebecca Jean Alonzi, 34, says she developed a dependence on sugary foods to fuel long nights building her farm-to-office food-service company Nourish Inc. As orders rolled in from Silicon Valley startups to cater their office spreads, she gained 30 pounds. She joined Overeaters Anonymous and got on a track to lose weight. Then she found herself having trouble focusing. A psychiatrist diagnosed her with attention-deficit hyperactivity disorder in 2012 and prescribed Adderall, a stimulant, which she says made her “skinny, bitchy and very productive.”

Within a year, she began having headaches and quit Adderall, concluding that amid building a health-food company she was hurting her own body. “I cared so deeply about making a difference that I was willing to push myself past my limit,” she says. “What I later learned is there are ways to achieve superhumanity that didn’t involve self-sacrifice.” Ms. Alonzi groomed a new CEO who took over this year, but she remains involved at Nourish as a chef-entrepreneur focused on new projects. She now incorporates into her routine “regenerative” activities like deep breathing, walks without a cellphone and barefoot hikes.

While many entrepreneurs find ways to deal with the pressure, some become increasingly destructive.

Brandon Truaxe’s hyperenergetic tendencies helped him build a cult beauty brand with hundreds of employees. Mr. Truaxe ran much of Toronto-based Deciem Inc. himself, sleeping little and using ephedrine and caffeine, said Riyadh Swedaan, his boyfriend of 11 years.

As the company grew, the pressure mounted. Mr. Swedaan said Mr. Truaxe started using crystal methamphetamine around early 2018, leading to increasingly erratic behavior. In October, Deciem investor Estée Lauder Co. took legal action, alleging that Mr. Truaxe had made hundreds of “disturbing posts” on Deciem’s social-media accounts, including threats, and leased a private plane and a new headquarters without consulting Deciem’s board. A spokeswoman for Deciem declined to comment.

The lawsuit led to Mr. Truaxe being removed from the company. He was hospitalized three times last year as a result of hallucinations from heavy drug use, twice in London and once in Canada, said Mr. Swedaan, who blamed the drugs for Mr. Truaxe’s downward spiral.

In January, Mr. Truaxe died after falling from his 32nd-floor condo.

An oft-cited issue in tech circles is that many startups fail because of people problems, not business issues. In a 2016 study, 92% of more than 13,000 venture capitalists surveyed by the National Bureau of Economic Research identified the management team as the most important factor in startup failures. “It is shocking how often startups fail because of the personality flaws and deep-seated traumas of their founders and execs,” said Garry Tan, managing partner at startup investor Initialized Capital, in a tweet.

The investments, sometimes billions of dollars, riding on founders’ ability to function keep many from talking about their struggles, says Ben Tauber, a Silicon Valley executive coach at Velocity Group. “If you talk with anyone, they say they are killing it,” Mr. Tauber says. Meanwhile, “inside they are dying.”

One common reason for distress, he says, is that founders and startup executives tend to derive much of their sense of self-worth from their company’s success.

“I think people are unprepared for how hard and awful it is going to be to start a company. I certainly was,” said Parker Conrad, the ousted former CEO of Zenefits, which achieved a $4.5 billion valuation in 2015 before running into numerous problems. Mr. Conrad, who now runs a human-resources software startup called Rippling, said stress-eating would cause his weight to soar during a big fundraising.

“I remember crying alone in my bed,” says Alan Gertner, 35, a former Google executive who left in 2015 to go into the cannabis business. When he sold his startup Hiku Brands, a Canadian marijuana retailer, last year for hundreds of millions of dollars, he said he felt little joy, only flickers of relief.

Founders often have more influence over their companies’ creative and strategic trajectories than leaders of established firms. As a result, their struggles can have outsize business consequences.

In 2017, major backers of Uber Technologies Inc. demanded the ouster of founder Travis Kalanick following a spate of scandals; Mr. Kalanick acknowledged that he needed to grow up. He declined to comment through a spokesman.

Discord between the two co-founders of HQ Trivia and the subsequent death of one of them, Colin Kroll, from a drug overdose threw the once-hot game-show app into disarray. “The company went through a difficult time following this horrible loss, but the core team has banded together,” said Rus Yusupov, HQ Trivia’s other co-founder, in an emailed statement.

Startup executives use a variety of “hacks” to stay mentally fit. Kimbal Musk recommends everyone “leave the planet” in some way; he slow-scrambles eggs as a form of morning meditation and goes to Burning Man every year. Several CEOs, including Zillow CEO Richard Barton, write in gratitude journals every morning.

Ms. Yang, formerly of Fuhu, has created LifeGyde and Second Time Founders, two startups focused on fostering healthy growth at young companies. “The health and well-being of the founder amplifies to their employees,” she says.

Through the grind of building Twitter from a scrappy startup to a public company, its former CEO Dick Costolo says he amped up his workouts: running, CrossFit, handstands, anything that could take his mind off work. Managing the stress was a persistent mental-health challenge, the 55-year-old said. “I had to do things to create a space in myself. I was constantly obsessing. You wake up at 3 a.m. in the morning and say, ‘What am I going to do about this?”

Mr. Costolo stepped down in 2015, two years after taking Twitter public, and is now an adviser to high-growth startups, counseling founders to try to maintain an evenness during the highs and lows.

Mark Pincus says his time at social game-maker Zynga has been an emotional roller coaster of sometimes extreme stress. He likened a founder to a war general tasked with telling his troops that they have to abandon safety, face the gunfire and run to the next foxhole. The 53-year-old says triathlons, surfing and weekly coaching on personal and professional matters has helped him navigate challenges. After jump-starting a turnaround, Mr. Pincus stepped down as CEO and later relinquished voting control to become nonexecutive chairman.

In part to help founders manage tough transitions, Mr. Pincus is on the cusp of unveiling a new venture fund called Reinvent Capital to fund companies through second acts and encourage founders to stay involved as entrepreneurs-in-chief.

A few venture-capital firms are now focusing more on developing founders as human beings rather than just CEOs.

“The prevalent view of startup founders in Silicon Valley is a delusion that in order to succeed, in order to build a high-growth company, you need to burn out,” says media mogul Arianna Huffington, a startup investor, Uber board member and CEO of her own wellness-focused company, Thrive Global.

Alpha Bridge Ventures has created a program to help support founders’ well-being. Kari Sulenes, its executive director, says digestive and autoimmune disorders can be exacerbated by stress. Founders’ “expectations for health are so low that even when they have something like Lyme disease, they think that’s just something to push through,” Dr. Sulenes said.

For Etsy’s Mr. Dickerson, the pressures eventually did mount. Two years after the IPO, the stock had dropped more than 30% from the listing price and the board fired him. After a low period, he gradually came to appreciate life as it was, thankful for his old experiences and ready to share his knowledge with others. Now he’s an executive coach.

“A whole new world kind of opened to me. I wasn’t rushing to the subway, wasn’t thinking about some deal,” he says. “I was able to bring my mind into the place that I was.”