Soaring automobile repair costs are expected to cut into the insurance underwriting profits of Geico Corp. this year, Chairman John Byrne told stockholders at the annual meeting yesterday.

Although Geico officers now expect the current gasoline shortages to resuit in fewer accidents, the rising claim costs from accidents that do take place are expected to wipe out any savings from less automobile driving, he said in response to a question.

Similar trends developed during the Arab oil embargo of 1973-1974 but, at first, state insurance regulators and many companies saw only the reduced accident rates and ordered reduced premiums because insurance profits were expected to benefit handsomely.

As it turned ots were expected to benefit handsomely.

As it turned out, the regulators were wrong as were many of the industry executives, including those in charge at the time of Government Employees Insurance Co., the big automobile insurance firm here that recently became the principal subsidiary of Geico Corp.

With rates too low to cover soaring repair costs, Geico almost sank into bankruptcy in a scare that shook the national industry. Byrne noted yesterday that the industry as a whole suffered losses of $9 billion during what many regulators had expected to be a season to "windfall" profits.

Today, with Geico Corp.'s financial condition rated strong and reserves to cover policyholder claims at a record $421 million, Byrne said he sees no major difficulties ahead.

He did not forecast overall profitability for Geico Corp., which earned a record $88.2 million in 1978. He did say that overall profits probably could not be improved substantially until Geico begins to increase its base of business, which apparently stabilized in recent months after a decline in customers that began during the firm's financial crisis earlier in the decade. Senior Vice President William Snyder forecast "modest growth.

Geico directors voted a quarterly dividened of 8 cents a share on common stock payable June 29 to owners of record June 12, and Byrne said in response to a question by professional stockholder George Sitka of Bristol Conn., that "the rate increase in dividends will more than keep up with inflation." Geico raised the quarterly payout to 8 cents from 5 cents last February.

Two directors did not stand for re-election, having reached retirement age: former Geico chairman David Lloyd Kreeger and former ambassador to Switzerland Shelby Cullom Davis. Davis, who did not attend the meeting, recently raised questions about possible conflicts related to Geico and affiliated firms, but Byrne said yesterday that reports by auditors and others to date indicate there is no substance to the allegations. A board committee's review of the questions is due shortly, Byrne added. CAPTION: Chart, Nationwide Gasoline Prices