NEW YORK, JUNE 15 -- The stock market gained ground for the sixth straight session today, riding out some afternoon selling as interest rates bounced around erratically.

The Dow Jones average of 30 industrials rose 13.81 to 2391.54, creeping nearer to its record closing high of 2405.54 set on April 6. Over the last six trading days, the average has climbed 65.39 points.

Volume on the New York Stock Exchange came to 156.92 million shares, compared with 175.07 million in the previous session.

Analysts said the market benefited early in the session from a stabilizing dollar and declining interest rates.Rates later turned upward in the credit markets, then pulled back.

Despite inflation and interest-rate worries, brokers said investing institutions seemed eager to increase stock holdings before their midyear reports at the end of this month.

Though stocks have been showing healthy gains lately, analysts say the market faces a challenging period later in the week in the quarterly "triple witching hour."

In a new twist, some of a group of expiring stock-index options and futures will be settled at the opening on Friday, rather than the close.

Thus, brokers say, if activities of program traders engaged in multiple strategies involving options or futures and individual stocks result in wide swings in the markets, that volatility could start to set in on Thursday and continue into Friday.

In today's trading, blue chip volume leaders included International Business Machines, up 3 at 159 5/8; Eastman Kodak, up 2 1/4 at 84 7/8; General Electric, up 3/4 at 54 5/8, and American Express, up 1/8 at 35 7/8.

Ford Motor, subject of positive comments in a Barron's magazine article, gained 3 3/4 to 97 1/8.

Bank stocks were a standout group. Citicorp rose 1 to 62 7/8; Chase Manhattan 1 3/8 to 43 1/2; J.P. Morgan 1 to 51 1/2; Chemical New York 1/2 to 45 3/4, and Bankers Trust New York 1 1/2 to 54 1/4.

Advancing issues outnumbered declines by about 5 to 4.