The stock market continued its dramatic climb today as investment funds poured into stock exchanges with few signs of a slowdown.

The Dow Jones Industrial Average rose another 21.88 points to close at 891.17, a gain of 103 points over the last six trading sessions. The Dow transportation average surged more than 13 points today to 337.31, a gain nearly doubling, in percentage terms, the rise in industrials.

Volume on the New York Stock Exchange continued at levels that startled veteran market observers. More than 111.4 million shares were traded today, the second-biggest volume in exchange history. The record was set last Wednesday when 132 million shares changed hands.

The transportation stock rise was particularly encouraging to market watchers, who said the gain is an indication that railroad traffic may pick up sharply as a broad economic recovery leads to rising industrial shipments.

In general, however, the bond markets stayed lower today as many analysts suggested that a number of large institutions had yet to be persuaded that the market's move is an indicator of an improving economy. There was also disappointment among bond traders that an expected one point cut in the discount rate failed to materialize.

"There is still a lot of skepticism in the market despite this move," said Michael Metz, senior vice president at Oppenheimer and Co. Inc. "But the higher it goes the more they are afraid they will miss something."

Metz, however, noted that there remain "enormous amounts of money not committed" to stocks and bonds, an indication that the rally is likely to continue. "There is enough money out there to support considerable extension of this move," Metz said.

The market shot up about 10 points early in the day, but by mid-afternoon the industrial average was up only about four points. But after that selling pattern ran out of steam, the industrial average, a gauge of blue-chip stocks, jumped by 17 points in the last two hours of market activity.

The most active stocks rose sharply, led by four of the nation's giant business concerns--Exxon, which rose by 5/8, Sears, Roebuck, up 1 3/8, General Motors, up 1 7/8, and International Business Machines Corp., up 1 1/8. Of almost 2,000 stocks traded today, 1,353 advanced, while 348 declined in price.

On the American Stock Exchange, volume also rose sharply to 6.9 million shares, up from 5.7 million Friday. While the average share price rose by 26 cents, 455 stocks rose, while 172 fell. The Amex index rose 6.20, closing at 261.72, with energy and technology stocks leading the way.

Meanwhile, over-the-counter trading was just as spirited with the Nasdaq composite index up 2.92, closing at 169.88. MCI Communications Corp. jumped by 3 3/8 with a final bid of 44 1/8, and computer concerns, Tandem, Intel and Apple Computer, all recording sharp gains. graphics /chart: The Market