Mstislav Rostropovich opened his third season as music director of the National Symphony Orchestra last night at the Kennedy Center, leading the orchestra in the opening concert of its 49th year. He began things with a rousing reading of "The Star-Spangled Banner," which many of the large audience joined.

His formal program took off with William Schuman's power-packed American Festival Overture, which will celebrate its 40th birthday in two weeks. It easily holds its place as one of the best pieces of music any American composer has written.

There were some new touches to be heard in the overture, as is often the case any time a top conductor takes up a work he has not previously conducted. While the outer sections went with all their usual fiery spirit, Rostropovich found some new voices and accents in the quiet middle of the overture. It was altogether a beautiful performance.

The remainder of the evening was Russian, with the brash, breezy Ninth Symphony by Shostakovich, and the First Symphony of the youthful Tchaikovsky. The sound theory that every composer foreshadows his mature style in his early works was proven in both of these symphonies.

Often during the Shostakovich Ninth there were passages that looked directly back into the heart of his First Symphony, written two decades before. But the later symphony, written immediately after World War II, has an assurance about it, to say nothing of a willingness to be lighthearted, even nose-thumbing. That perky theme in the opening movement is perfect impure Shostakovich.

There are beautiful solos scattered through the symphony, and after its strong conclusion, Rostropovich walked through the orchestra and beckoned to the solo bassoon, piccolo and violin to stand and acknowledge the applause with him.

The orchestra was in fine form all evening. This was not a seasonal opening after which to apply the phrase, "It is too early to discuss the orchestra's merits." The musicians sounded at a real peak, with the brass choir in shining form and the strings frequently of a special sheen.

At intermission, board president Austin Kiplinger brought onstage two players who are retiring after this week's concerts: cellist Franz Vlashek, who has been in the National Symphony for 27 years, and percussionist John Kane, a member for 17 years. The audience applauded them generously as it had before the program when Rostropovich had brought them out in front of their colleagues.

In the Tchaikovsky the process was reversed from that in the Shostakovich: Much in the lovely music strongly forecasts characteristic harmonies and instrumental textures that will be part of the fabric of the greatest Tchaikovsky to come. The slow movement, especially, presages the last act of "The Queen of Spades," while often there are pre-echoes of "Swan Lake."

The oboe in the slow movement was a thing of particular beauty, joined in a touching trio by bassoon and flute, over muted strings. The finale has problems in getting going, but none in reaching a roaring closing. The audience was shouting when it was all over. It made for a hearty beginning to the season.