The Dow Jones Industrial Average, which topped 900 for the first time in a year Tuesday, fell today in heavy trading.

The Dow average, the most widely followed stock market indicator, closed the day at 895.05, down 6.26 points on the day. Nearly 83.8 million shares of stock changed hands on the New York Stock Exchange today, well below the record 137.3 million set last Thursday but well in excess of the year's average daily volume of 55.4 million. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 97.68 million shares.

Standard & Poor's index of 400 industrials fell 1.57 points to 132.07, S&P's 500-stock composite index was off 1.26 points at 118.25, and the New York Stock Exchange's own index fell 0.64 point to 67.9.

The American Stock Exchange market value index fell 1.33 points to 278.69. About 5.14 million shares were traded compared with 7.54 million on Tuesday.

New York Stock Exchange Chairman William M. Batten and President John Phelan met with reporters here today to point out how well the nation's biggest stock exchange has coped with the tremendous trading volume of the last three weeks.

Phelan said the exchange and the brokerage firms are processing the huge trading volume easily and said the exchange could handle 200 million shares if it had to. Phelan and Batten said huge investments in computer systems made by the stock exchange and brokerage firms during the last several years have given the industry many more transactions and shares than it is handling now.

In 1968, when volume averaged 12 million shares a day and the peak trading day was 21 million, Wall Street nearly broke down because of a paperwork overload. The exchange's trading hours had to be curtailed, and several firms went out of business becuse they could not handle the mountain of stock certificates and trading slips.

But officials of several major brokerage firms said that Batten's and Phelan's confidence is misplaced. They said that improperly executed trades, which mount dramatically when volume rises, take about two weeks to show up. "We're not collapsing, but I see our operations department facing many more problems," said one official.

On Aug. 12, stock prices started a rally that has continued at a feverish pace, with occasional setbacks like today's. The rally was triggered by the sharp decline in short-term interest rates that started in late June and was aided by passge of nearly $100 billion in tax increases that are supposed to reduce the size of the federal budget deficit in coming years.

But investors, heartened as they may be by the propsect of lower interest rates, still see a bad economy, according to Jerry Hinkle, chief trader for the brokerage firm Sanford Bernstein & Co. "The realities are pointed out by General Motors cutting prices on 1983 models. Business is not picking up. Third-quarter profits will be miserable," Hinkle said.

Hinkle said that the stock market has been rambling upward on extended enthusiasm, a phenomenon brokers call "overbought," and that at some point the Dow average had to stop rising. He said that the catalysts for today's decline were the announcements by Chemical Bank and U.S. Trust Co. that they were raising the interest they charge brokers who borrow overnight funds from 10 3/4 percent to 11 3/4 percent.

Most analysts did not see the move as a signal of an upturn in other interest rates but rather as a result of the heavy demand for broker loans because of tremendous trading in the stock market.