The storied United Auto Workers union passed into the hands of a new generation today when Owen Bieber, 53, took the gavel of the presidency from Douglas A. Fraser.

The popular Fraser, who had served the union since 1936, was the last of a band of brothers who fought at the Depression barricades with the legendary Walter Reuther to mold the nation's third largest union into a formidable social and political force.

Bieber, relatively unknown both in and out of the union ranks, takes office under pressure to prove himself to a rank and file membership that is frustrated and bitter over recent "give-back" contracts, shrinking membership, declining political influence and other adversities.

In his first speech as president, Bieber made an emotional appeal for acceptance to the 2,500 delegates at the union's convention here.

"I was not on the battlefield during the great struggles of the 1930s," he said. "But, by God, I am a product, heart and soul, of what was created in those difficult struggles."

Citing a litany of economic, technological and other complex problems facing the union, Bieber added, "Just as the great struggles of the '30s shaped the last generation . . . , I believe the horrible problems we face today are shaping the new generation."

Fraser, playing against the sentimental grain of the occasion, chided the new, younger leadership team as he summoned them to the podium to take the oath.

"These guys don't even know how to line up yet," he said. "I'll straighten 'em out."

Fraser also took a parting shot at the Teamsters union. "I would not be comfortable being in the same labor movement as the Teamsters," he told reporters. "You get tarred with the same brush . . . , so corruption is a concern of ours."

UAW membership has declined to 1.1 million members from a peak of 1.5 million in 1979. The Big Three auto makers have lost billions as foreign imports grabbed almost one-third of U.S. auto sales. New technology is causing permanent reductions in the number of industry jobs. At the convention hall here, many delegates wore buttons reading "Restore and More," a reference to the contractual give-backs.

Bieber drew standing ovations whenever he talked tough about the union's future bargaining stance and organizing strategies.

He defended the concessions the union made to auto makers "even though they shook us to our very roots as a union. We made sacrifices, not because we lacked the guts to take the companies on, but because we possessed the wisdom to know we were better off . . . ."

But, he vowed, "We've given all we're going to give."

The delegates came to their feet cheering again when Bieber promised that the UAW will organize the Nissan truck plant in Tennessee and the Honda plant in Ohio, and especially when he pledged that GM-Toyota vehicles to be produced in Fremont, Calif., "will be built by UAW members--the members who worked in that plant when it was operated by GM."

Union leadership had made an effort to keep the convention from being distracted by presidential politics. No candidates were invited to speak, and Bieber made only a passing reference to the need to "dump Reagan." But he called on the delegates to "redouble our political action efforts between now and 1984, not just to recapture the White House, but the Senate as well."

When the convention delegates crowned Bieber by a voice vote Wednesday, they were following a script written for them last November, when top UAW officials endorsed him.

Typecast by many as a "Mr. Nice Guy" who lacks Fraser's flair and warmth, Bieber is also described as a hard-working, nuts-and-bolts man who appreciates the complexities of the modern world.

Bieber, until this week the union's General Motors vice president, worked his way up through almost every elective office in the union. His union career began in 1948 at a spring plant in Grand Rapids, Mich.

Fraser, whose tenure saw the union through both its brightest and darkest days, has traveled the country in recent months saying his goodbyes to UAW members. He resisted efforts to get him to bend the union's rule against running for office after the age of 65 because, he said, he believes in the rule. He made a wry reference to past union officials who stayed until they were in their 80s and 90s.

Fraser, who became president in 1977, will remain on the AFL-CIO Executive Council until October, and will retain his seat on the board of Chrysler Corp. for the next year. This fall he will join his predecessor, Leonard Woodcock, as a teacher at the University of Michigan.