Stock prices took a severe drubbing today -- one of the worst in history -- as sharply rising interest rates touched off a round of heavy panic selling.

The Dow Jones industrial average, probably the most closely watched market index, fell 26.45 points, its biggest tumble since Jan. 9, 1974, when the Dow dropped 26.99 points.

Meanwhile, trading volume on the New York Stock Exchange was the fourth heaviest in history as investors sought to unload their holdings. more than 55.9 million shares changed hands during the six hours of trading on the exchange.

Virtually no stock or industry escaped the wave of heavy selling. in all, 1,768 stocks closed lower today, while only 73 managed to rise.

The market had lost more than 13 points on Monday. As a result, the Dow Jones average, which closed near the magic 900 level on Friday, has lost 40.02 points in two days of trading this week to close at 857.59.

Bond prices also took a beating, as they always do when interest rates rise.

As with stocks, bond prices fell across the board.

Robert Farrell, the top analyst for Merrill Lynch, Pierce, Fenner & Smith said the key to the market's action today was Saturday's moves by the Federal Reserve Board.

As part of its restrictive new monetary policy to restrain the growth of the money supply, the nation's central bank said it no longer will worry about how high interest rates rise.

On Monday, stock prices lost ground in anticipation of a big increase rates today.there was no banking to speak of in the United States Monday because it was Columbus Day.

This morning investor's fears came true as first Chase Manhattan Bank and then a host of others boosted their prime lending rates to 14 1/2 percent from 13 1/2 percent, and other short-term rates rose even more.

Most analysts say that if the Fed sticks to its guns, it will get the growth of the money supply -- and therefore, inflation -- under control. But in so doing it will precipitate a serious recession.

The stock market is facing a "tug of war" in its judgment about the Fed, said James Baylog, senior executive vice president of Drexel Burnham Lambert. Initially the market is worried about the short-term effect of a recession on companies and their profits, he said.

But there is a long-term "beneficial effect of getting the monetary aggregates and inflation under control," Baylog added.

He predicted that selling would stop soon after this initial panic and that the market will begin to rise again.

Merrill Lynch's Farrell said the steep decline of Monday and today don't signal a major, sustained fall in stock prices. "The decline is not over," he said. "It may extend into next week." But after that, stock prices should resume their upward climb, he said.

Although most stock prices were hit hard today, banking stocks took a terrible beating.High interest rates will increase the cost of funds for banks and the other Fed move to restrict the supply of money also will squeeze bank lending and profits.

Bank stocks also were hurt by a warning Monday from Comptroller of and Currency John Heimann that there could be bank failures of a result of the restrictive Fed policy.

For example, Chase Manhattan fell $3 a share to $37.125, Citicorp declined 75 cents to $22.25, Bankers Trust dipped $3.25 to $40.50 and Continental Illinois closed off $1.875 at $26.

Prices also fell sharply on the American Exchange, with its index off 12.26 points, the largest one-day decline since the second-biggest stock exchange began compiling it in 1973. The Amex index closed at 220.15. On the Amex, 759 stocks closed lower, while 36 rose.

Things were no better in the over-the-counter market. Most issues declined, and the National Association of Securities Dealer's NASDAQ index was off 5.78 points at 145.20.