The stock market kept moving ahead today with a late burst of buying that carried the Dow Jones industrial average to its first close ever above 1,400.

The widely recognized average of 30 blue chips climbed 6.77 to 1,403.44, extending its gain since mid-September to more than 105 points. Other, broader market measures remained below their mid-summer highs, but they continued to push closer to those levels.

Volume on the New York Stock Exchange picked up to 129.48 million shares from 119.20 million Tuesday.

Analysts said falling interest rates have raised hopes on Wall Street for a strong economy in 1986. Interest rates have taken a tumble in the credit markets of late. In today's trading, rates were generally mixed, with small changes.

Lower rates would presumably act as a stimulus to spending for construction and capital equipment, giving debt-laden consumers some help in keeping the economy growing. At the same time, falling rates reduce the relative appeal of interest-bearing investments such as bonds, which compete with stocks for investors' favor.

Marvin Katz of Sanford C. Bernstein predicted the market would continue to move higher and said the investment public is just starting to get interested in buying stocks. He said leveraged buyouts and "merger mania" show that business already understands the value of corporate assets.

Harry Villec of Sutro & Co. in San Francisco said the market is still undervalued. He said after the Dow's move, the market might back off a little. But he said it would resume its upward move and hit 1,500 by the end of the year.

The Dow Jones industrial average touched 1,400 early in the session and again at midday, pulling back each time amid selling by some traders who had planned in advance to do so at that round-number level. But stocks came on strong again just before the close.

Wall Street also got a boost early today from International Business Machines, which said it expects to post "some strong growth" in the current quarter. IBM shares rose 5/8 to 132 7/8 in active trading.

Among other leading computer and technology issues, Hewlett-Packard gained 1 1/4 to 32 1/4; Texas Instruments 4 1/2 to 94 3/4, and National Semiconductor 1 1/8 to 11 5/8.

Scientific-Atlanta added 1 to 11. The company said it expects to report higher earnings for the current fiscal quarter, and is likely to recommend that directors increase the dividend within the next 12 months.

Contributors to the Dow's advance included McDonald's, up 1 at 70 7/8 and trading at record highs; American Express, up 1 3/8 at 47 1/4, and American Can, up 3 at 61 3/4.

Fireman's Fund, whose shares were recently sold to the public by American Express, rose 7/8 to 30 1/2. The company declared a quarterly dividend of 7.5 cents a share.

Allied Stores rose 2 3/4 to 61 5/8. The company declined comment on a published report that it plans to sell five regional shopping malls.

Advancing issues outnumbered declines by about 3 to 2 on the Big Board. The exchange's composite index gained 0.24 to 111.31.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 153.20 million shares.

Standard & Poor's index of 400 industrials rose 0.39 to 214.03, and S&P's 500-stock composite index was up 0.39 at 192.76.

The Nasdaq composite index for the over-the-counter market picked up 1.49 to 296.74. At the American Stock Exchange, the market value index closed at 231.20, up 0.96.