Stock prices rose sharply in heavy trading today, as institutional buyers rushed to buy securities.

But analysts could pinpoint no particular factors triggering the buying surge.

The Dow Jones Industrial Average closed at 859.81, up 11.26 points. The Dow has stopped short of crossing the 850-point barrier five times in the past two months, but crossed that mark in early trading and continued to climb for most of the day.

Prices fell slightly during the final hour of trading.

Volume, which has been sluggish in recent weeks, registered a strong increase. Nearly 45.6 million shares of stock changed hands on the New York Stock Exchange -- the second busiest day of the year, compared with 27.2 million shares on Monday.

Only 402 NYSE stocks declined in price today, while 1,144 were higher.

Newton Zinder, of E. F. Hutton & Co., said demand was strong for blue-chip stocks and top-tier glamor issues, an indication that institutions were the major factor in today's buying binge. Institutions are partial to these types of stocks, such as Du Pont and IBM.

Institutions have been putting little money into stock investments and have been husbanding large cash reserves, keeping their money in assets such as Treasury bills.

Prices were up at the American Stock Exchange as well, where trading is not dominated by institutions as it often is on the New York exchange. The Amex index closed at 199.43, up 0.24 from Monday. Zinder said that while he expects the stock market to trade in a higher range than it has been for the last few months, he anticipates no broad, sustained rally for several months.

"I anticipate the Dow will trade between here (850) and 880 for a while," Zinder said.

Analysts said that investors probably were encouraged by some sign that inflation pressures might be easing.

President Carter said earlier today that he thinks food price increases will continue to get smaller and new guidelines announced by the Council on Wage and Price Stability do not appear to be much looser than the ones announced last fall.

Paul Volcker, the new chairman of the Federal Reserve, and former Fed chairman G. William Miller, now secretary of the Treasury, have said that fighting inflation will remain the chief economic priority.

The most active issue on the New York exchange was International Business Machines, which closed up 1 1/4 to 70 1/2. More than 654,000 shares of IBM were traded.

IBM was one of nine stocks in the Dow sporting a gain of a point or more. General Motors climbed 1 1/2 to 59 5/8; Du Pont 1 1/2 to 43 3/8; Procter & Gamble 1 5/8 to 76 1/2; General Electric 1 1/8 to 52 5/8, and Eastman Kodak 1 to 55 5/8.

The market's strength and the increased trading activity sparked gains in the brokerage-house stocks. Merrill Lynch rose 5/8 to 20 1/8; Paine Webber 3/4 to 10 1/8, and E. F Hutton 1 1/4 to 19 1/2.

G/ Heilman Brewing, which voted a 50 percent stock dividend and an increase in its cash payout, picked up 2 1/4 to 39.

Vendo posted the day's biggest percentage gain, rising 1 to 6. The company reported second-quarter earnings from continuing operations of 32 cents a share, against one cent in the comparable period last year.

Deltona rose 7/8 to 13 3/8 on higher quarterly operating profits.

Greyhound, whose bus business is booming as a result of the gasoline situation, was the second most active issue, closing at 6 1/8, up 1/2. Slightly more than 600,000 shares of Greyhound were traded today.

On the New York exchange, 126 stocks reached new yearly highs while only two reached new lows. On Monday, when the Dow average closed up 2.39, 67 stocks reached new highs, while five reached new lows.

The New York Stock Exchange common stock index closed at 60.18, up 0.73 from Monday's close. CAPTION: Graph, The Market, August 8, The Washington Post