Profits from operations of Geico Corp. were flat last year but rose in the final quarter, the Washington insurance firm reported yesterday.

Not counting gains or losses from investments or an extraordinary tax benefit in 1979, Geico earnings last year were $59.6 million compared with $59.5 million the previous year. Per-share profits rose to $2.59 from $2.14 because of repurchases of shares that reduced outstanding common stock to 23 million shares from 27.8 million.

In the fourth quarter alone, operating profits rose to $15.4 million (70 cents) from $13.6 million (53 cents).

Chairman John Byrne said property and casualty-written premiums rose 5 percent, life insurance premiums were flat and investment income increased 6 percent. Byrne characterized the results as "overall a little better but not yet exciting."

Geico reported an investment gain of $1.1 million last year and an investment loss of $723,790 in 1979. In addition, Geico had a $15.4 million tax benefit in 1979 that reflected losses in the mid-1970s. Thus, net income in 1980 was $60.8 million ($2.64) vs. $74.3 million ($2.67) the previous year.

"It took skillful management to achieve profitable underwriting results in 1980, as it will again in 1981," said Byrne of his holding company's major product line, automobile insurance. "Although our customers are having fewer accidents, inflation is wreaking havoc with automobile repair costs."

Property and casualty premium volume was $638.6 million last year compared with $606.3 million in 1979. Geico said more details will be available in the annual report, due to be mailed about March 13.