The Dow ended the day up 25.88 points, or 0.2 percent, to 16,504.29.
"The very narrow range reflects that there's not a lot of news out there and a lot of investors' positions are closed for the year," said Alec Young, chief global strategist with S&P Capital IQ.
The Standard & Poor's 500 index fell less than a point to 1,841.07 and the technology-heavy Nasdaq composite fell 2.40 points, or 0.1 percent, to 4,154.20.
Walt Disney rose $1.88, or 3 percent, to $76.23, the most in the S&P 500. Analysts at Guggenhiem Securities upgraded Disney's stock to a "buy" from a "hold" on Friday.
With just one trading day left in the year, 2013 is looking to be a memorable one for investors. The S&P 500 is up 29.1 percent so far, on pace for its best year since 1997. The Dow is up 26 percent, the most since 1996.
With 2013 in the books, investors have turned their attention to the beginning of 2014. Few expect next year to be as good to investors as 2013 was.
"After a year like this, people start to think a 30 percent-plus year is normal," said Ron Florance, deputy chief investment officer for Wells Fargo Private Bank. "We need to be realistic going into next year."
The next big piece of news investors will have to work through will be the December jobs report, which will be released Jan. 10. There is also corporate earnings season, which will start in the second half of January. Corporate earnings will be important, particularly since this upcoming season will encompass the closely watched holiday shopping period.
"The market is rallying on the idea that economic growth is picking up globally and in the U.S., so investors need to see those expectations matched," Young said.
Bond yields continue to tread water around the 3 percent level. The yield on the U.S. 10-year note fell to 2.98 percent Monday from 3 percent Friday.
The market is expected to be a holding pattern until next week, once all the mid-week holiday disruptions are over, Florance said. Both the NYSE and the Nasdaq Stock Market will be closed Wednesday for New Year's Day.
In overseas markets, Japan's Nikkei stock index closed higher for a ninth straight day Monday. The index ended 2013 up 57 percent. Japanese markets will be closed Tuesday for New Year's Eve.