Mead Corp. decided yesterday to quit being the last hold-out in a three-year class action by announcing that its board of directors had approved a tentative $45 million settlement to end litigation in which Mead had been found guilty of fixing prices on corrugated shipping containers.

The settlement ends a bitter legal battle for Mead, which has fought the price-fixing charges ever since the suit was filed in 1979.

"Our decision to settle the case out of court was especially difficult because we believe the company and its people have obeyed both the spirit and the letter of the law," said Mead's chairman, Burnell R. Roberts. However, the "decision to settle was based solely on the conclusion that it is in the best interest of our shareowners to settle the case rather than to pursue costly and protracted litigation," Roberts said.

The settlement will end the class action that involved 37 cardboard manufacturers and more than 200,000 plaintiffs. Of the defendants, all but Mead had settled out of court for payments totaling $320 million -- a sum that now is worth more than $400 million with interest added.

Mead refused to settle, however, contending all along that it was innocent and repeatedly pointing out that a federal jury found Mead innocent of criminal price-fixing charges in 1979.

Even so, a jury hearing the civil class action found Mead guilty of price-fixing in 1980. Mead is awaiting a court judgment on how much it should pay in damages as a result of the verdict. But some lawyers have estimated that the damages could be as high as $750 million because, under the antitrust laws, as the only company to be found guilty in the suit, Mead would be responsible for paying all of the damages incurred by the industrywide price-fixing scheme, even though the company has only a 2.5 percent share of the cardboard box market.