Chanting "No nukes" and singing the civil rights anthem "We Shall Overcome," about 120 rain-drenched antinuclear protesters were arrested today as they marched onto the grounds of Virginia Electric and Power Co.'s nuclear plant here.

The carefully planned demonstration, one of the last of some 45 anti-nuclear protests held around the nation and in several other countries over the weekend, was staged to protest the plant's operation, which demonstrators charged threatens human life. Demonstrations also were held today in West Germany, France, and Spain, where a protester was killed.

Both Virginia and Louisa County police started to make the arrests as the protesters arrived at the perimeters of the plant and stepped through the gates onto Vepco property.

According to Vepco vice president C.W. Stallings, who called the protest "foolishness," the 20 or so people on duty running the one operating reactor at the plant continued their work without incident.

None of the various placard-carrying groups of protesters got within 250 yards of the reactors at this rural central Virginia plant about 85 miles southwest of Washington.

Yesterday's demonstration - involving about 13 local antinuclear and environmental groups, all calling themselves the Virginia Sunshine Alliance - was the culmination of a weekend of rallies and protests near the plant that drew, altogether, about 900 people.

About 200 demonstrators, many wearing armbands signifying that they intended to be arrested, gathered early this afternoon at the entrance to the plant's access road and marched the 1 1/4 miles to the main gates.

Moving along the sides of the only road leading into the plant, the protesters held their hands high over their heads, occasionally clenching fists in a sign of greeting to supporters as they neared Vepco's property.

Protesters then split into several small "affinity groups," each attempting to gain peaceful entry onto the plant site. One group surrounded a power line's tower and sat down. Others ducked under gates or lined up against a fence bordering the restricted area of the plant.

While state police used bullhorns to warn the demonstrators they faced arrest for trespassing, many of the protesters linked arms in the rain and chanted, "They people united will never be defeated."

As soon as protesters went through plant gates, waiting sheriff's officers handed them summonses. Those arrested, the vast majority of them young people, seemed almost relieved to get out of the downpour and into waiting police vans.

One of the last groups to be arrested, however, "went limp against a Vepco fence, forcing police to carry them into vans that took them to the Louisa County jail.

Elsewhere in the country, about 450 protesters went to jail in Shoreham, N.Y., after a demonstration at a nuclear power plant being constructed by the Long Island Lighting Co. Some of these used ladders to scale a barbed-wire fence in an unsuccessful attempt to occupy the plant, which is scheduled to open in 1981.

In the town of Madison in north-western Indiana, another 89 protesters were arrested at the Bailly I plant owned by Northern Indiana Public Service Co. At the Marble Hill plant in southern Indiana, 100 demonstrators were arrested. In Moscow, Ohio, 25 demonstrators were arrested at the Zimmer Nuclear Power Plant.

In Plymouth, Mass., a day-long Clamshell Alliance rally drew about 5,000 people who listened to anti-nuclear speeches and danced to rock bands in the shadow of the Pilgrim I plant. There were no incidents or arrests.

In northern Spain, a woman was shot and killed as police clashed with 2,000 people protesting the construction of a $1 billion American-supplied nuclear power plant in the north Basque city of Balboa, the Associated Press reported. Police said the woman was killed when a civil guard opened fire with a submachine gun on stone-throwing demonstrators.

[About 8,000 turned out for an anti-nuclear demonstration in Kalkar, West Germany, and 3,000 for a rally at a plant site in the French province of Brittany, the AP reported.]

On anticipation of the weekend protest, officials at Virginia's North Anna plant shut its visitors center for the week and erected new "No Trespassing" signs and fences on the property. They also met with state police and with leaders of the protest to establish elaborate guidelines for the demonstration.

"I can't think of anything of this magnitude that's ever taken place in Louisa County before," said Charles Vaughan, a state police spokesman.

In addition to the equal numbers of protestors and police, more than 60 reporters and photographers were no hand to record the event. Vaughan said FBI and Maryland authorities also came to observe the demonstration.

Those arrested face fines of up to $1,000 and one year in jail for trespassing. Many demonstrators had vowed earlier to forgo any attempts at making bail and to stay in jail until an expected July 17 trial date.

Spokesmen for the antinuclear alliance passed out literature during the protest, condemning Vepco's safety record at its North Anna and Surry plants. They charged that both plants are technologically unsound and vulnerable to vandalism - allegations the utility firm strongly denies.

Only one of Vepco's four nuclear reactors is now in operation. Three others - two at the Surry plant and one at North Anna - are shut down for repairs.

The only speechmaking on the danger of nuclear power took place not yesterday but at a rally the day before, at a drive-in theater near Louisa, not far from the North Anna facility. There, former antiwar activist Elizabeth McAllister had urged people to challenge of what she called the nuclear age.

"All of us are sitting on this [nuclear] train, and it's moving," said McAllister, who is the wife of former priest Philip Berrigan. "But we don't know who is the engineer or who planned the trip." CAPTION: Picture, An antinuclear demonstrator is arrested by Virginia and Louisa County officers at Vepco's North Anna nuclear plant. UPI