Most major banks raised their prime lending rates dramatically today, from 13 1/2 percent to 14 1/2, and all other short-term interest rates skyrocketed as a result of the Federal Reserve Board's tough, new anti-inflation monetary policy.

It was the first business day since the Fed announced the new policy last Saturday and "it was chaos," said Patrick Savin of Drexel Burnham Lambert Inc.

Some short-term interest rates rose more than 1 1/2 percentage points during the day.

At the same time, stock prices plummeted in heavy trading, with the Dow Jones industrial average falling 26.45 points. It was the biggest decline in that closely watched barometer since the beginning of the 1974-75 recession.

Last Saturday, the Federal Reserve said it no longer would try to control the growth of bank reserves by controlling interest rates. Instead, the agency said, it would worry directly about the rate of growth of bank reserves themselves and let short-term interest rates go where they may.

That direction was sharply upward today.

The federal funds rate, which used to be the interest rate the central bank tried to control, rose to about 13 percent. Friday, when the central bank was still using the federal funds rate as a guide to monetary policy, the rate was in the 11 1/2 to 11 3/4 percent range.

At one point in the hectic day, federal funds were being offered as high as 18 percent.

The federal funds rate is the interest banks charge each other for overnight loans of excess reserves. Other short-term rates include such things as 90-day Treasury bills rates, commercial paper and certificates of deposit.

Chase Manhattan Bank, the nation's third largest, touched off the prime rate rise and was followed quickly by most other banks. Chase cited continued strong loan demand as well the rising cost of funds.

Because banks must purchase in the open market much of the money they then lend to customers, rising market interest rates force them to boost the interest they charge for loans.

The banks' problems are compounded because the Federal Reserve not only stopped trying to stabilize open market rates, it also put new reserve requirements on many of the sources of bank funds, such as large certificates of deposit.

A bank must set aside 8 percent of all the funds it gets by selling a CD. The bank cannot earn interest on that 8 percent reserve, which makes the cost of borrowing to the bank and to the customers higher.

Edward L. Palmer, chairman of the Executive Committee at New York's largest bank, Citibank, said the new Fed policies produce "a great deal of uncertainty about where interest rates will be."

In the past, the Fed would buy and sell government securities to keep enough funds in the system to support its target rate. Now, Palmer noted, "the interest rates will depend solely on demand for funds."

As a result, Commercial Credit Corp. economist Leon Gould noted, there will be many volatile swings in interest rates, as there were today.

"Today's was only the initial response," Gould said. "Further increases in rates are likely and they are likely to be sizable."

Citicorp, for example, sells commercial paper every Tuesday morning (commercial paper is essentially a corporate IOU). Citicorp owns Citibank.

Last Tuesday, Citicorp had to pay an interest rate of 12.208 to induce other corporations to buy $150 million. Today, to sell the same amount, Citicorp said an interest rate of 13.994 percent.

The new Federal Reserve policy is designed to discourage borrowing by making the cost of money higher and to cut down on the supply of funds in the system.

In trying to maintain a federal fund rate, the central bank often found itself pumping more money -- albeit expensive money -- into the system than it wanted to. As a result, the money supply -- checking accounts and currency in circulation -- rose sharply.