Just after the opening bell, the Dow Jones industrial average was up 47 points at 13,159. The Standard & Poor's 500 index was up four points at 1,421. And the Nasdaq composite index was up three at 3,003.
Technology stocks and energy companies were among the early winners. Apple gained $4.08 per share to $588.70, building on a gain from Monday after the company said its newly released iPad Mini was practically sold out.
Among other stocks making big moves, Computer Sciences jumped 13 percent, the most in the S&P 500, after the company's earnings blew past analysts' estimates. The stock was up $3.72 at $35.18.
Weight-loss company Medifast rose $1.77 to $28.59 after reporting that its third-quarter earnings increased more than 40 percent as expenses fell and the company got strong responses to its ads and new programs.
Express Scripts dropped $9.87 to $53.01. The pharmacy benefits manager warned that persistently high unemployment and economic uncertainty would hurt its business next year.
Trading was relatively light Monday, and financial analysts said they expected it to be light again Tuesday.
More than anything, analysts say, investors want the election behind them. The certainty of a winner will allow Wall Street and Congress to focus on the so-called fiscal cliff, tax increases and government spending cuts that take could effect Jan. 1.
It figured to be a quieter Election Day for the market than last time. On Nov. 4, 2008, during the financial meltdown, the Dow shot up 305 points, easily the biggest election rally of all time. Investors expected a victory for Barack Obama.
On Election Day 2004, the prospect of a close election led to a late sell-off, and the Dow finished down 18 points, snapping a five-day winning streak. John Kerry didn't concede to George W. Bush until the following day.
In the bond market Tuesday, the yield on the benchmark 10-year U.S. Treasury note dipped 0.02 percentage point to 1.70 percent as investors moved money out of bonds and into stocks.
The price of oil climbed 82 cents per barrel to $86.47 in New York trading.