WARSAW -- Poland's voters poured out by the millions Sunday and cast their ballots in what the official news agency PAP called "an atmosphere of calm, seriousness and responsibility" in the first partially democratic elections here in more than 40 years.

When the polls closed at 10 p.m., PAP hailed the balloting as a "new chapter of socialist parliamentary democracy."

Official results may not be available for two days, but preliminary indications were that candidates backed by Solidarity were beating Communist candidates by huge margins in those races where head-to-head contests were allowed.

An elderly woman voter, referring to the Communist-controlled elections of the past, said after casting her ballot: "It feels totally different. Now there is freedom of choice."

It was the first time since a national election in January, 1947, that Poles were given a meaningful choice among candidates, though political power will remain with the ruling Communist Party under an agreement with the Solidarity trade union and other opposition forces.

A total of 27.2 million Poles were eligible to choose among nearly 2,300 candidates for 525 contested seats in a new bicameral legislature. Poles in foreign countries cast absentee ballots at embassies and consulates around the world.

More than 73% of the eligible voters cast ballots, a StateElectoral Commission spokesman said early today.

For some the choice was bewildering. In rural areas, some voters, especially elderly and ill-educated farmer folk, were confused over the voting procedure, according to local poll watchers. Voters were presented with as many as seven paper ballots and were instructed to cross out the names of candidates they opposed.

'Too Many Names'

In some places, people had to cross out more than 100 closely printed names of candidates for various posts to pick their choices. "Too many names," complained one rural voter. "People are getting lost. They don't know who is who."

However, most voters seemed well coached on the complicated process of selecting candidates. Many reported that they were voting for the first time in 40 years.

"It's important this time," said one man outside a suburban Warsaw polling station. "This time something could change here."

For 48 cloistered nuns, the election was a rare venture into the mundane world. They had received special permission to vote at a Warsaw polling station. One made a broad, sweeping sign of the cross before dropping her ballot into the ballot box marked with Poland's national colors, red and white.

If the election can be viewed as a referendum on four decades of Communist rule, as most Solidarity supporters contend, it seems likely to turn out as an embarrassing rout for the authorities of Poland, whose list of 35 candidates for the national Parliament were failing to win election, even though they were running unopposed.

Solidarity leader Lech Walesa warned against an overwhelming defeat of the Communist slate and its supporters, fearing a backlash by hard-liners that would set back Poland's march to greater democracy.

Single Red Rose

Wearing a single red rose tucked in the breast pocket of his coat, Walesa, his wife, Danuta, and their 19-year-old son, Bogdan, walked 100 yards from their home in the Oliwa section of the Baltic port city of Gdansk to the polling station to cast their ballots.

"Poland has started on the road to progress," Walesa told a throng of cheering supporters. But he cautioned that when the elections are over, "the hard work will begin. That is why we should stick to moderation."

Polish leader Wojciech Jaruzelski, whose regime had at one time outlawed Solidarity and sent Walesa to prison, cast his ballot in the Mokotow district of Warsaw, spending three minutes to make his choice.