The stock market yesterday finished the best week in its history.

The Dow Jones Industrial Average rose 30.72 points, ending a week that saw the index rise 81.24 points, its biggest weekly gain ever. The Dow finished the week at 869.29.

Volume on the New York Stock Exchange this week was 455.8 million shares, also a record. There were more shares traded on the New York exchange this week than changed hands in all of 1953.

The extraordinary rise in the stock market was attributed to this week's continued slide in interest rates and passage of President Reagan's $98.3 billion tax bill.

Major banks yesterday continued to lower their interest rates, with Chase Manhattan dropping its prime lending rate from 14 to 13 1/2 percent. Other banks, including American Security Bank in Washington, quickly followed.

The prime rate, the interest rate banks charge their best corporate customers, has dropped 1 1/2 points this week and 2 1/2 points in the last six weeks. The prime is at its lowest level since October, 1980.

Open-market interest rates also continued to fall, with the rate on federal funds, charged on loans between major banks, trading at 8.75 percent yesterday, off from 15 percent little more than a month ago.

The interest rate on $100,000 three-month certificates of deposit, another major source of funds to banks, was about 9 percent yesterday. And financial markets were rife with rumors that the Federal Reserve might be about to cut the discount rate for the fourth time in a month. The discount rate is charged by the Fed on loans to member banks.

The Federal Reserve Board reported yesterday that the nation's money supply fell $100 million to $453.4 billion in the week ended Aug. 11, indicating that the central bank now has more leeway to ease credit conditions.

The Fed has been supplying more money to the banking system in recent weeks as money supply growth has stayed within its targets. Some analysts believe a shift in Fed policy in response to the weak money supply figures has been behind the decline in rates over the last six weeks.

Consumer loan rates have also started to ebb, with mortgage rates falling sharply in the past week, although not to levels that would significantly revive the nation's battered housing market. Details on Page D7

Analysts gave lower interest rates credit for the stock market's skyrocketing performance this week. Many said the trigger was the prediction earlier in the week by influential Salomon Brothers economist Henry Kaufman that interest rates would continue to drop.

"The big news is the decline in interest rates," said Hildegard Zagorski, an analyst at Bache Halsey Stuart Shields. Analyst Monte Gordon of Dreyfus Corp. said the effect of the prime rate cuts was accentuated by the frequency of the reductions. "I think that happened more quickly than people expected it would."

The market has reacted favorably to the interest-rate decline despite the fact that the drop is the result of the overall weakness of the economy. "The market has blocked out the unfavorable aspects of why the interest rates have gone down and focused on the favorable aspects," Gordon said. "The market is enjoying its good news right now."

In addition to the decline in interest rates, analysts said the rise in stock prices yesterday was helped by the passage of the tax package in Congress. Wall Street believes the package will help the economy. "I think that set the upside juices flowing in the morning," Zagorski said.

"The president's relatively easy victory in the Congress [Thursday] solidified opinions that we have both sides of the aisle in the Congress and the administration with similar goals: stimulating the economy, cutting the budget deficit, reducing spending," said Robert Stovall, an analyst at Dean Witter Reynolds.

Stovall suggested that the passage of the tax bill and the strong showing of the stock market in recent days could signal economic recovery. "It looks as though you've got the political and financial legs in place, all you need is some signs of a business recovery, an earnings recovery," he said. "You've got interest rates, food and fuel prices down, that's helped the inflation [figures] and you've got stock and bonds markets up, and that's good for psychology."

Other analysts weren't as optimistic, however. Newton Zinder of E.F. Hutton suggested that the stock market rally would temporarily peak next week, and then prices could fall sharply in late September or early October when it becomes clear that economic recovery is not at hand.

"By then there will be more realization that the economy is not recovering and that it is still weak," he said.

In other economic news yesterday, the Commerce Department reported that new orders at U.S. factories for durable goods such as machinery and furniture rose 3.2 percent in July after falling in the three previous months. Analysts called the increase, the biggest in almost two years, another sign that the economy may be reviving.