The ride hailing app began trading as a public company at $42 (£35) per share on Friday, nearly 7% below its initial public offering price.
The firm had priced its IPO cautiously at $45 (£34.50) a share, giving it a market value of $82.4bn (£63.1bn) ahead of its debut on the New York Stock Exchange.
As well as ferrying passengers around, Uber delivers food to its 91 million customers.
More than 5.2 billion trips were completed using Uber last year – delivering food and giving rides to its 91 million passengers.
Despite this, the California-based company has lost about $9bn (£6.9bn) since its inception and has warned it could be years before it makes a profit.
The IPO price was already almost a third less than what investment bankers had predicted last year, with Uber settling for a lower valuation amid a series of investor concerns including profitability and the lukewarm reception for rival Lyft’s market debut.
Lyft went public six weeks ago – but its share price has tumbled by more than 20% from its IPO price set in late March.
Although the company’s co-founder Travis Kalanick was ousted as chief executive two years ago, his outstanding stake in the business was expected to be worth $5.3bn (£4.1bn).
He was spotted on the trading floor of the NYSE as the bell was rung in the presence of his successor, Dara Khosrowshahi.
Uber has faced several controversies in recent years – including claims of sexual harassment within the company and allegations that it stole self-driving car technology.
The firm was also accused of covering up a computer break-in that stole personal information about its passengers.
Some Uber drivers have also been accused of assaulting passengers, and one of the company’s self-driving test vehicles struck and killed a pedestrian in Arizona last year while a back-up human driver was behind the wheel.