Harold Solomon and Guillermo Vilas, who have had some lovely little wars on clay courts on both sides of the Atlantic, advanced today to a semifinal meeting in the U.S. open tennis championships.

Solomon, the No. 12 seed from Silver Spring, Md., who had never been past the round of 16 here, played superbly in eliminating old rival Dick Stockton, the No. 10 seed, 6-4, 6-4, 6-2.

Vilas, seeded No. 4 but riding the momentum of a summer-long rampage, opened the stadium program on a gorgeously clear and cool Indian Summer day by stomping Ray Moore, 6-1, 6-1, 6-0, in just 80 minutes.

Vilas has not met Solomon during his current six-tournament winning streak, which dates to mid-July and now spans 37 matches, during which he has lost only four sets.

Vilas is 1-0 over Solomon this year, having beaten him in the quarterfinals of the American Airlines Tennis Games on California cement in April, and has a 6-4 lifetime advantage.

But Solomon is 3-2 on clay, the surface on which Vilas has won 44 matches in a row, starting with the French Open.

The 5-foot-6, 140-pound man with infinite patience beat Vilas in the French the two years they played there - in the third round in 1972 and the quarterfinals in 1976. "Those were the two times we've played best-of-five sets," Solomon said today. "I think he's got a little psychological block about that. I think I should probably be favored."

Vilas has lost only 16 games in beating Manuel Santana. Gene Mayer, Victor Amaya. Jose Higueras and Moore, and most people rate him along with the victor in Thursday's Jimmy Connors-Manuel Orantes quarterfinal as the favorites for the title.

The Argentinian lefthander's performance today had to enhance his backers' confidence. From the first game he was on top of the ball, ripping outright winners from the backcourt, thumping approach shots, devouring volleys and overheads.

His onslaught was so furious that Moore, the good-natured and universally popular 31-year-old South African who answers to the nickname "Hippie," raised his arms triumphantly when he finally held his serve for 1-3 in the second set, ending a seven-game Vilas run.

The crowd cheered sympathetically as Moore beamed, but his respite from the topspin flood was brief. He did not win another game.

Vilas started the year with insatiable hunger for a major title. "I wanted to win one of the big ones," he says, "because it was a strange thing - I was all the time in the top players, but the only one who never won a big tournament.Nastase did, Connors did, Borg did, Orantes did, Panatta did, and I didn't. I was the only one."

He went to Melbourne to play the Australian Open, but lost in the final to Roscoe Tanner. Then in June he won the French, which relieved the enormous mental burden of being considered at home as "The Eternal Second."

That first Grand Slam title whetted his appetite, and he has played hungrily ever since. "How do I feel? It's the same as a guy who never eats. One day he eats bread, the next day he wants a sandwich, the next day he wants a steak and the next day he wants to go to the palace," Vilas said today.

"It's more or less the same. Once you win one big title, you want to win another one, and if you won two you want to win the third one, and then you want them to build a statue in the middle of Buenos Aires."

Solomon is not thinking in terms of statues in Silver Spring, but he says, "I think I have as good a chance as anybody to win this thing."

He played today very much as he did in beating Italian Open champ Vitas Gerulaitis Monday - getting a high percentage of first serves in, hitting his ground strokes consistently deep and moving exceptionally well to cover drop shots.

Solomon kept the 6-foot-2 Stockton pinned deep, unable to take advantage of his aggressive net game. Stockton hung in patiently through many back-court rallies, but Solomon won almost all of them, hitting so deep that he eventually got Stockton to hit while backing up, and those were the ground strokes he missed.

Stockton won a number of points when he got to the net on his terms, but he couldn't do it often enough. And when he threatened to get into a serve-and-volley rhythm, Solomon was able to crack his returns hard and make them dip with topspin, forcing volleying errors.

Solomon broke serve in the first game of the match and made that stand up for the set. He missed only four of 30 first serves and established control from the backcourt with positive, attacking strokes.

Solomon broke for a 2-1 lead in the second set, blasting a backhand down-the-line passing shot on his third break point after Stockton had come back from 15-40 and gotten the advantage with an ace.

Stockton threatened briefly to get into the match when he held for 2-3 after Solomon had won four straight points from 40-0, then broke at 15 in the next game, held for 4-3, and had 0-30 on Solomon's serve.

But Solomon pulled out of that hole with a nice forehand down-the-line pass and three Stockton errors - a backhand volley, a wrong-footed forehand from the baseline and a netted drop shot.

Solomon broke at 15 in the next game, as Stockton netted two backhands and another backing-up forehand after a vicious forehand cross-court pass. Solomon was off on an eight-game romp and did not let up until he was ahead, 5-0, in the final set.

"I think that was one of the best matches Harold Solomon has ever played," said Dennis Ralston, the former U.S. Davis Cup captain who now is tutoring Stockton, Roscoe Tanner and Brian Gottfried, who plays Corrado Barazzutti in another quarter-final Thursday.