Interest rates tumbled yesterday for the second day in a row, apparently because of an easier monetary policy by the Federal Reserve.

Another major bank cut its prime lending rate to 10 3/4 percent from 11 1/4 percent, and the rest of the banking industry is expected to follow suit within a matter of days.

The steep decline in interest rates sparked a massive rally in the stock market. The Dow Jones industrial average climbed nearly 35 points to close at 1211.57. Nearly 170 million shares of stock changed hands in frenetic trading on the New York Stock Exchange. Story on Page B3

The easier Federal Reserve money policy apparently is aimed at preventing the recent slowdown in economic growth from turning into a recession. Analysts said the central bank also would like to foster lower rates in an attempt to weaken the dollar. The strength of the U.S. dollar has discouraged U.S. exports and encouraged imports, producing massive trade deficits and making it hard for some industries to recover from the 1982 recession.

Two years of relatively low inflation apparently have convinced the central bank that rising prices are not a major problem and that it can ease up on policy without triggering a return to high inflation.

Analysts and investors expect the Federal Reserve to lower its discount rate -- the interest it charges member banks for loans -- as a signal that it is encouraging lower rates. But the central bank, which has permitted rates to slide precipitously since late Friday, yesterday kept the discount rate at 8 1/2 percent.

Open market rates declined markedly, however, although the fall was more striking in overnight money than in longer-term funds.

The federal funds rate -- the interest banks charge each other for overnight loans of excess reserves and the interest rate the Fed can influence most easily -- fell as low as 6 1/2 percent yesterday and ended the day at about 6 3/4 percent.

Only last Friday, the federal funds rate was close to 8 1/2 percent.

Most analysts said yesterday that, probably for technical reasons, the federal funds rate has fallen farther than the Fed wants it to or than monetary policy would justify.

Other money market rates such as the interest banks must pay on large certificates of deposit reflect the market's belief that the central bank wants the federal funds rate to be about 8 percent and that the federal funds rate will return to that level soon, according to Douglas Ledwith, chief financial officer of American Security Bank.

For example, banks had to pay about 8 1/4 percent to sell 30-day certificates of deposit. Nearly all money market rates were down about 25 basis points -- a basis point is one one-hundredth of a percentage point -- except for the federal funds rate, which was down nearly 100 basis points.

The federal funds rate is a rate on which nearly all other money market rates are based. Analysts said that a discount rate cut from 8 1/2 to 8 percent would tend to validate the market belief that the Fed has targeted 8 percent for federal funds. A bigger cut in the discount rate, say to 7 1/2 percent, would encourage the lower federal funds rate that prevailed yesterday and probably would bring down other money market rates, according to William Sullivan, vice president and chief money market analyst for the securities firm Dean Witter Reynolds.

Sullivan said other banks will have to follow the lead of Manufacturers Hanover Trust Co., which Monday cut its prime lending rate to 10 3/4 percent. Manufacturers, the nation's fourth-biggest bank, was followed yesterday by Bankers Trust Co., the nation's ninth-biggest.

The spread between a bank's cost of funds and the prime lending rate is very large, and banks have dragged their feet on lowering the prime rate in order to boost profits in a time of difficulty in the industry. According to Sullivan, regulators have subtly encouraged banks to go slow in reducing their rates, to enable banks to build up reserves against problem loans.

Sullivan said that, based on historical data, even a 10 3/4 percent prime rate is high, let alone the 11 1/4 percent prime that is in effect at most banks. The prime rate is the interest charge on which most short-term business loans are based.