Stock prices continued their sustained 16-week climb, as the Dow Jones Industrial Average closed up 3.75 points today and 23.31 points on the week.

Analysts and others who have been looking for an end to the strongest stock market rally in years were unable to find it again this week, although prices weakened substantially today in late trading.

Since April 13, the Dow average of 30 major industrial stocks has climbed about 25 percent, from 763.40 to today's close of 954.69. That is the highest level that barometer has reached since March 18, 1977.

An increasing number of Wall Street analysts, including those at Merrill Lynch & Co., the world's biggest securities firm, believe that stocks again have become a first-rate, long-term investment -- if for no other reason than they are "cheap" when compared to other assets.

Nevertheless, even when the long-term direction for stock prices is "up," that movement comes in fits and starts, with a rally followed by a decline that is followed by another rally.

A 16-week rally is long by historical standards and some sort of "correction is long overdue," according to Phil Roth of E.F. Hutton & Co. But each time stock prices have slipped, and they have declined several times since the rally started April 13, a new wave of buying sent prices climbing again.

Stock prices increased sharply in late trading Thursday and started off smartly today. Shortly after noon the Dow average was 10 points above its Thursday close.But prices gave up much of that gain in late trading and by the end of the day both prices and trading activity had subsided.

Market observers expected, on the basis of earlier trading activity, that about 10 million shares of stock would change hands during the final hour of trading. Trading volume during the last hour on the New York Stock Exchange totaled slightly more than 7 million.

Still, 59.1 million shares were bought and sold today, only slightly fewer than the 62.6 million shares traded Thursday.

Bill Blankenburg of Advest Inc. said the late price declines meant little. "It's Friday," he said. "The retreat [in stock prices] was a very natural kneejerk response to a good week."

The New York Stock Exchange composite index closed up 0.21 points to 70.81, an all-time high. The American Stock Exchange index was up 2.28 to 319.41 points.

On the New York Stock Exchange, 899 stocks closed higher while 635 closed lower.