The stock market continued its dramatic advance today as the Dow Jones Industrial Average, rising nearly 26 points, climbed over the 1,000 mark for the first time in 18 months.

It was the second busiest day ever on the floor of the New York Stock Exchange, with 138.5 million shares traded. The record was set last Thursday when volume hit 147 million shares. The Dow Jones index closed at 1,012.79.

Wall Street analysts were hesitant to credit the Reagan administration for the boom in stock prices. Instead, they attributed much of the current market rise to falling interest rates as a result of an easing in monetary policy by the Federal Reserve Board. The Dow industrials have risen more than 105 points since the start of last week.

"The market is not going up because of Reaganomics," said William LeFevre, vice president-investment strategy at Purcell, Graham and Co. "The market is going up because of falling interest rates and interest rates are declining because the economy is in such bad shape. The market is bubbling because of his failure."

Another highly regarded analyst, Michael Metz of Oppenheimer & Co., said it is "simple-minded to think there is any one factor" pushing up stock prices. President Reagan, Metz said, "contributed to it when he abandoned supply-side economics last August" and agreed to raise taxes. "His pragmatism allowed the Fed to begin a loosening process. He contributed to it in that sense."

At one point, during a frenetic trading day, the market was up 34 points, creeping up to over the 1,020 mark, although many traders later sold their holdings and took profits. The all-time high for the Dow industrials was set on Jan. 11, 1973, at 1,051.70; today's advance brought the average to its highest point since April 28, 1981, when it closed at 1,016.93.

Lower interest rates have had two positive effects on stock prices. First, lower interest rates improve the picture for corporations and stock prices are predominately a measure of business profitability. Secondly, the rate drop has also forced down the amount of interest that can be paid out in money market funds and, therefore, investors have turned to the stock market in hopes of maintaining high investment returns.

Many analysts here predict the market's momentum will keep stock prices rising through the remainder of the year, though not at the same pace as in recent days. Richard McCabe, a vice president of Merrill Lynch, Pierce, Fenner & Smith Inc., said the Dow Jones index is likely to stall in the 1,000 to 1,050 range. He said he expects the market to drop back, then resume its upward move.

The market gains had been primarily as a result of run-ups in the stocks of the large corporations that are used in compiling the Dow. Although today's gains were led by those big companies, such as New York exchange trading leader American Telephone & Telegraph Co., which rose by 1 1/4 to 62 3/4, Exxon, which was up 1 3/8 to 30 5/8, and International Business Machines Corp., which rose 2 3/8 to 83 1/2, others began following suit today.

In particular, the securities of companies that stand to benefit from lower interest rates, such as auto manufacturers, banks, and brokerage houses, rose sharply. Merrill Lynch, for instance, was up 3 3/8 to 46 7/8, while Paine Webber jumped 2 3/8 to 29 3/8.

On the banking front, Chase Manhattan Bank rose 1 1/2 to 46 1/2, while Bankers Trust was up 2 3/8 to 42 5/8. In autos, General Motors jumped 2 7/8 to 52 5/8, and Ford rose to 30 7/8, up 1 7/8. Even stocks related to the depressed housing industry benefited, as, for instance, Weyerhaeuser rose 1 1/4 to 33 3/4 and Georgia Pacific rose 1 3/4 to 23 3/4.

Nearly 1,500 stocks on the New York exchange advanced and only 282 fell in per share price, with the average price per share up 79 cents. Standard & Poor's measurement of 500 stocks jumped 3.42 to 134.47.

On the American Stock Exchange, the gains were also broad, although trading dropped slightly from last Friday's market. The Amex index was up 4.95 to 304.49, with volume at 8.6 million shares, down from 9.4 million on Friday.

The NASDAQ composite index for the over-the-counter market closed at 202.31, up 3.42 points.