The American flag flies high over idyllic Prybil Beach here, and if the Russians ever try to rush the facility, they will have to come by way of the sea, and not from the direction of the sandy shore.

The Russkies, who have a summer place in this lush town on Long Island, have been banned from the sandy shore. Likewise, they've been banned from the municipal golf course and the fishing pier, and the two tennis complexes, three of which, the mayor proudly notes, are illuminated for nighttime play.

Espionage explains it all, the locals say. They claim that the Russians are using their 49-room mansion here to spy. Nor have the entreaties of the State Department--nor the involvement of the big guns in the Justice Department--managed to sway the feelings in this little town. This week, after voting in May to ban the Russians, the town council voted again, 6 to 1, to keep the Russians off the courts. And if the State Department feels that's meddling in foreign affairs, and some folks consider the ban petty, the mayor of Glen Cove demurs.

"The word petty infers that there were several courses of action which could be taken, and we felt we no other course to take, the only thing we could do which would have an effect was to revoke their recreational pass," said Alan M. Parente. "We'd like them to leave Glen Cove and short of that we'd like them to stop spying, and we took the only actions open to us."

Meanwhile in Washington, the Soviet government, the dog days of August on the horizon, spoke of reprisals: "The city of Glen Cove has shown their understanding of what hospitality is all about," said Soviet Embassy press officer Vladimir Mikoyan, "and of course, if resolution of this regretful incident faces a deadlock, we might be forced to take retaliatory steps against the Americans in the Soviet Union."

It was starting to sound, somewhat, like the arms race, he was told.

"Yes," he laughed. "And you see, you started it, America once again started it."

The Russo-Glen Cove cold war, which may or may not evolve into an international incident, has already resulted in some embarrassment among State Department officials. It dates back, historically, to April, when the town of Glen Cove first learned of the alleged espionage by reading about it in the Newsday, the local paper. They learned that the Russians had installed surveillance equipment in the top three floors of Killenworth, a 37-acre estate.

There have been, however, according to students of the Russo-Glen Cove scene, tensions among the two peoples long before that. The Russians have been residents of Glen Cove since the creation of the United Nations, and they have long been resented by the Glen Covians for their tax-exempt status. The reports of espionage, according to Mayor Parente, were the last straw.

"We were quite upset and sent off a number of letters to the FBI, the CIA and the State Department, requesting information," he said. "We got a letter from the FBI indicating that it was common knowledge that just about every mission has some intelligence activities; they were all very general letters, indicating that nothing could be done . . . . "

In Glen Cove, they did something. They voted to rescind the recreational rights of the Russians. The Russians, who reportedly included some fairly devout tennis players, did something, too. They went to the U.S. Mission to the U.N. adviser Sol Kuttner and told him that the Glen Covians had "asked they turn in all of their passes."

The mission reported to the State Department. The State Department promptly dispatched a note to Glen Cove. "Discriminatory actions such as those taken by Glen Cove interfere with the conduct of foreign relations in the United States," it said in part. The mayor said the City Council would act on the matter at their next meeting. This week, the City Council met. They voted 6 to 1 to keep the status-quo.

The only optimistic note for a ready solution--before Americans are likewise banned from the courts in Moscow--is in one statement from Mayor Parente. He says he's writing to the State Department that he is "hopeful that an immediate and meaningful dialogue can be initiated between the State Department and my office so that this issue can be quickly and amicably resolved." That is to say, that though they're a power on Long Island, Glen Cove is willing to sit down with the little guy and talk.