Under elaborate security arrangements which have been in force all week, the United States and South African Davis Cup teams yesterday went through the final day of preparations for their controversial meeting in the American Zone North Section final.

The three-day, best-of-five match tennis series is scheduled to begin tonight at Memorial Gymnasium, on the campus of Vanderbilt University. Vitas Gerulaitis was drawn to play South Africa's Bernie Mitton in the opener, followed by Harold Solomon of Silver Spring, Md., against Byron Bertram.

While demonstrations protesting the aparthed racial policy of the South African government have not gained nearly the numbers or momentum predicted by the civil rights groups organizing them, the emotional politics of the anti-South Africa movement have aroused high anxiety here.

The stringent security measures - including uniformed and plainclothes guards at the gymnasium and the hotel where both teams are headquartered - serve as a reminder that attempts to disrupt the matches, while not anticipated, are a possibility.

"We've got a lot of nervous people around here," said Ed Fabricius, public relations director of the U.S. Tennis Association, which, with a local committee, has responsibility for staging the matches.

"The city is up-tight. The people on campus are up-tight. They'll all be glad when this thing is over and we go away."

Small demonstrations are planned tonight by student groups and an ad hoc organization called the Tennessee Coalition Against Apartheid.

The major protest of the weekend, however, is planned for tomorrow, before and during the doubles match expected to pit Fred McNair of Chevy Chase, Md., and Sherwood Stewart against South Africans Bob Hewitt and Frew McMillan.

Demonstrators will march from the Tennessee state house to Memorial Gym, a distance of three miles, and then on to Centennial Park, six blocks away.They have been granted a permit to stage an anti-apartheid rally there.

Benjamin Hooks, executive director of the National Association for the Advancement of Colored People (NAACP), said yesterday he was "hoping for at least 2,000 people to participate."

That is a far cry from the 40,000 demonstrators predicted six weeks ago by Charles Kimbrough, president of the Nashville chapter of the NACCP.

Hooks, who had promised "the largest demonstration this country has seen since the 1960s," yesterday told The Washington Post that this group had "deliberately decided to go for representation rather than mass participation.

The protests will be peaceful and orderly and will not attempt to discrupt the matches, Hooks said, adding that "this is intended to be an educational effort, to focus the attention of the American people on the situation in South Africa and show them the evil we're up against there - the racism and repression that the South African government has no intention of changing."

"We could have organized buses, caravans and planeloads of people if we thought we needed tens of thousands to make our point," Hooks said, "but our decision was a matter of husbanding resources."

There will be no picket line set up at the gym, which players and spectators would have to cross, as had been considered, and the demonstrators will be too far away during saturday's rally to interrupt the matches with chants.

Nevertheless, the political activity appears to have succeeded in discouraging ticket sales. The local organizers, who had hoped to raise substantial revenue for the Vanderbilt tennis program from gate receipts, now fear that they will not draw the 4,000 spectators per day they need to break even financially.

Fewer than 7,200 tickets had been sold as of yesterday afternoon, and original attendance projections of more than 20,000 have been cut in half.

"Everyone's scared. They haven't sold nearly as many tickets as they had hoped because people are afraid to come out," said Solomon. "I heard they couldn't even give them away at one point. Parents wouldn't let their kids come to the matches because they were afraid.

"I think it's all been blown way out of proportion by the press. We haven't seen any incidents or problems at all. I really don't think it's going to be as big a deal as it's been made out."

Solomon, 25, who has played Davis Cup for the United States in Romania and Chile, said the security precautions and tension were greater in those countries.

"The 1972 final in Romania was the worst," he said. "It was right after the Olympic massacre at Munich and we had two Jewish guys on the team, myself and Brian Gottfried. We had guards with machine guns following us around everywhere."

Gerulaitis, 22, who represented the U.S. in Venezuela in 1976, said that the fact that practices this week were closed to anyone without proper credentials had a psychological impact.

"Not an outward effect, but it was different," he said. "There's a little tension, like everybody's waiting for Doomsday to come on Friday. Nobody knows what to expect."

The U.S. is heavily favored to win the series since Ray Moore, the topranked South African singles player, withdrew two weeks ago, saying he did not want "to participate in something that turns a sporting event into a political demonstration."

Hewitt and McMillan, the reigning U.S. Open and Granx Prix Masters doubles champions, will be favored to give their team one point, but ranking and past records are with the Americans in all four singles.

Solomon plays Mitton in the fourth singles on Sunday, while Gerulaitis and Bertram are paired in the finale.

Gerulaitis is ranked No. 3, Solomon No. 14, Bertram No. 68, and Mitton No. 110 in the computerized rankings of the Association of Tennis Professionals.

"But Davis Cup matches are completely different from tournaments. Anything can happen," said Claude Lister, the Englishman who serves as nonplaying captain of the South African team. "There's a special excitement to playing for your country and it can inspire a player. That's important in these long matches, best-of-five sets with no tie breaks."

Solomon - who trained hard last week in Florida, practicing six hours a day, running and doing exerices - was bothered by tendinitis in his right knee early in the week, but says it has responded to Butazolidin and other anti-inflammatory medication prescribed by team physician Omar Fareed.

U.S. Captain Tony Trabert said both his singles players should be in top form going into the matches on a medium-pace synthetic court at Vanderbilt. Light balls, well suited to both Solomon and Gerulaitis, will be used, with changes after the first seven and every nine games thereafter.

Gerulaitis had not played Bertram and is 1-0 over Mitton during the last three years, Solomon is 2-2 lifetime against Mitton, having won the last two, and has never lost to Bertram.