Harold Solomon and Vitas Gerulaitis will be the singles players named later this week by Captain Tony Trabert to the U.S. Davis Cup team scheduled to play South Africa in Nashville May 17-19.

Solomon, 25, of Silver Spring, Md., who is playing in the $225,000 U. S. Pro Indoor tennis championships here, said yesterday that Trabert has promised the singles berths in the best-of-five match series to him and Gerulaitis, the reigning Italian and Australian open champ who has never played Davis Cup singles.

Two teams are under consideration for the doubles: Gerulaitis and Sandy Mayer, the surprising 1975 Wimbledon champions, and 1976 Grand Prix Masters champions Sherwood Stewart and Fred McNair IV of Chevy Chase, Md.

The North American Zone final, first of four series the United States would have to win in order to recapture the prestigious 78-year-old trophy won by Australia last year, is scheduled indoors on a synthetic court at Vanderbilt University. However, a number of anti-South Africa demonstrations are planned and may disrupt the match.

Some Vanderbilt officials are reportedly sympathetic to the protests against South Africa's apartheid policies and nervous about allowing use of their facilities for matches involving an official South African team.

South Africa was barred from Davis Cup play in 1971-72 but was readmitted in 1973. It won the cup in 1974 when India refused to play the final.

A number of nations refused to enter the competition this year because of South Africa's inclusion, and grdowing demands for her ouster in future years will be considered at the annual meeting of the Davis Cup nations in June.

The present South African team includes Bob Hewitt, Frew McMillan, Ray Moore, Byron Bertram and Bernie Mitton. Moore and Bertram are expected to play singles against the U.S., Hewitt and McMillan (twice Wimbledon and current U.S. Open champions) the doubles.

If the series takes place as scheduled, it will be the same weekend as the final three rounds of the $125,000 Volvo Classic in Washington. Solomon had expected to play in that tournament before being selected for Davis Cup.

Solomon was on the U.S. team in 1972-73-74, compiling a 4-3 record in zone singles matches, including a critical five-set victory over Juan Gisbert in a 3-2 triumph over Spain at Barcelona in 1972. That got the U.S. to the final in Romania, where it last won the cup. Solomon did not play in Bucharest.

Solomon was miffed at being passed over in favor of Brian Gottfried when the U.S. lost to Mexico, 3-2, in the second round of the 1976 competition. That series was played on clay, a surfact that favors Solomon's persistent, patient backcourt game, and he said afterward that he would never play for Trabert again unless he were guaranteed a singles spot.

Trabert sent a form letter to all the top American players, outlining the prospective dates of the four series, and asked each player's availability. Few wanted to play the South Africa match, but Solomon said he would be available for all not played on grass - a surface on which he is ineffective.

"I'd like to play. We have a good enough team that we should win it," said Solomon, adding that compensation for U.S. players had not yet been worked out.

He said he had "an understanding" with Trabert about the singles. "As far as I know, Gerulaitis and I were the only one he considered for this match," Solomon said.

Stewart and McNair, who were ranked No. 1 in the U.S. in doubles last year, are a more experienced team than Mayer-Gerulaitis, but Mayer would provide Trabert more flexibility in singles should Solomon or Gerulaitis become ill or injured. Neither Stewart nor McNair is highly ranked in singles.

Stewart and McNari are 1-0 in Davis Cup doubles, having won a first-round 1977 match against Venezuela in Caracas.

The U.S. has been considerably frustrated in Davis Cup play since losing the 1973 final to Australia, 5-0, in Cleveland. It has failed to win the American Zone since, losing to Colombia in 1974, to Mexico in 1975 and 1976, and to Argentina last year.