Two major manufacturers of personal computers have reported sharp increases in sales during the Christmas season and said sales should continue to grow in 1983.

The computer industry as a whole--and small, so-called personal computers in particular--has bucked the severe recession that has gripped much of the rest of the economy. Special tax benefits for those buying personal computers for business or trade use helped boost December sales, as customers hurried to beat the Dec. 31 tax deadline.

Tandy Corp., which owns Radio Shack, said its December sales were a record $372.8 million, 23 percent higher than in December 1981, and that it expects sales in the last three months of 1982 to show an increase of 20 percent over the final three months of 1981.

Commodore International Ltd. said that its sales in the final three months of 1982 were more than $175 million compared with $70.1 million in the last three months of 1981.

In an interview with Dow Jones News Service, Tandy Chairman John Roach said that sales have continued strong in the days following Christmas. "We have been pleased--almost surprised--with the strength of sales. They are looking very good," he told Dow Jones. But Roach would not be specific about the sales level.

He said that, on the basis of December's sales, he is comfortable with estimates by Wall Street analysts that Tandy would earn between 85 and 90 cents a share during the company's second fiscal quarter, which ended Dec. 31. That translates to about $90 million in profits. The year before, Tandy earned $73.8 million in its second quarter.

Commodore Chairman Irving Gould also said that he is optimistic about his company's immediate future.

He said "Commodore's sales are continuing at a very strong rate, a trend that is expected to continue into fiscal 1984 which, like Tandy's, will begin July 1, 1983 . As a result, we look for both the current quarter ending March 31, 1983, and fiscal 1983 ending June 30 to be record periods," Gould said.

Commodore's VIC-20 personal computer--with a list price of $299--was perhaps the best-selling personal computer last year. Analysts said that as many as 1 million of the units were sold to consumers last year.

Tandy's TRS-80 Model III, at $999, once was the most popular personal computer, in large part because of the immense Radio Shack distribution system. But Tandy's share of the market has declined as the number of competitors and the intensity of competition has escalated.