The sight of the Acropolis, suspended for centuries between a gleaming white rock and an equally dazzling sky, is as awe-inspiring as ever. But a growing number of Americans seem to be wondering whether it is worth even the slight risk of getting caught up in the cross fire of Middle East terrorism.

On three separate occasions this year -- the TWA hijacking last June, the Achille Lauro affair last month and now the Egyptair killings -- American travelers have been killed simply because they were American.

Here in Athens, the starting point for the two airplane hijackings, U.S. citizens are beginning to feel the kind of pressure that comes from being a terrorist target. It seems symbolic that TWA shares a special high-security gate in the airport departure lounge with El Al, the Israeli airline which leads the world in antiterrorist precautions.

In TWA's downtown offices, clients are scrutinized by armed security men from the moment they set foot in the building. Even stricter security precautions are in force at the U.S. Embassy, which earlier this month was the target of what has become an annual demonstration by students protesting American support for the Greek junta that was deposed in 1974.

Reactions among Americans traveling in Greece to the latest outrage and its sequel on the tarmac of Malta airport have ranged from cheerful indifference to near panic. Interviewed as they were about to board planes for destinations ranging from London to Melbourne, some passengers dismissed a possible hijacking as a minor risk associated with what is still one of the safest forms of transportation.

But a significant proportion, almost certainly larger than would have been the case in a similar random poll a few months ago, expressed fear. Some said they would seriously reconsider future travel plans in the light of the latest incidents.

"We have been traveling for six weeks. Now all we want to do is to get home in one piece, alive. Our friends will probably have a nervous breakdown when they find out we have been in Athens," said Val Coleman, a former Maryland resident on his way back to Australia with his wife and daughter.

Charles Freund, a free-lance writer from Washington, canceled a planned trip to Cairo at his wife's insistence after hearing about the Egyptair hijack. They opted instead for Rome, a safer sounding destination. "The emotional stress was too great," Freund explained.

By contrast, Tom Allen, a bearded 26-year-old backpacker from Virginia, shrugged his shoulders when told about the hijack.

"I like this life. If I get killed along the way, that's just too bad, I guess. There are worse ways to go," he said.

In Athens later in the day, the twisting, narrow streets of the Plaka district beneath the Acropolis reverberated to the sound of loud American voices joking about the possibility of a surprise trip to Malta. They belonged to a group of Ohio students who planned to stop over elsewhere in Western Europe on their way back to the United States.

Predictably, younger Americans take the risks of traveling much lighter than those with family responsibilities. According to Greek tourist officials, the State Department's travel advisory had most impact on the richer tourists. The warning, issued on June 18, was withdrawn on July 22 after Athens airport was inspected by the U.S. Federal Aviation Administration.

The official U.S. reaction to the latest hijacking from Athens airport has been mild in comparison to the diplomatic storm that erupted after the TWA affair. The moderate tone reflects an assessment by the FAA that the Greek authorities have taken significant steps to improve security at the airport.

Western diplomats here said that there is no proof that the arms used to hijack the Egyptair plane were smuggled on board at Athens airport. The alternative possibility -- that they had been hidden on the plane at Cairo -- is equally, if not more, plausible, according to diplomatic analysts here.

In Washington, Secretary of State George P. Shultz described the security arrangements at Athens airport as in line with international standards.

George Papadimitropoulos, governor of the Athens airport, told Reuter that the FAA had warned airlines last week to be alert for the possibility of terrorist attacks.

[Transportation Secretary Elizabeth Dole said on NBC-TV's "Today" show that FAA investigators "are going right now" to check both Athens and Cairo airports. "Obviously there was something amiss here," she said, "but so much has been done at the Athens airport to strengthen the security there."]

Much of the criticism this time has come from West European countries. The French National Airline Pilots' Union urged a boycott of Greek airports, and similar calls have been made by British members of Parliament and the West German interior minister.