Already stunned by soaring gasoline prices, car owners now face the prospect of sharp increases in auto insurance rates - increases that will push the cost of owning and operating a car to record levels.

Major insurance companies say the cost of car repair claims has jumped from 14 to 17 percent so far this year and those costs will quickly produce higher rates.

State Farm Mutual, the nation's biggest car insuror, yesterday announced a 10.3 percent rate increase in Virginia, where Allstate Insurance received a 13 percent increase this spring.

Maryland drivers face an upcoming rate increase request from Geico, which like State Farm and Allstate reports double-digit inflation in auto repair bills.

The insurance rate rises are coming on top of gasoline price increases that the American Automobile Association says added four-tenths of a cent a mile to car costs in the first quarter this year.

By the AAA's calculations, it cost 18.3 cents a mile to own and operate an intermediate-sized car as of March.

Virtually all of the increase was due to gasoline prices, said AAA's Hank Downey, and since March gas prices have jumped another 10 cents a gallon.

"You don't have to be a graduate economist to presume the price of owning and operating a car has escalated even further since then," added Downey.

The AAA estimated that the 0.4-cent-per-mile increase recorded in the first quarter would add $60 a year to the car costs of a motorist who drives a V-8 powered intermediate car 15,000 miles a year and keeps it four years.

The car cost experts agree that a major factor in pushing the price of auto ownership to 20 cents a mile is the less obvious costs-like the added interest paid by financing a car for four years rather than three and the increased insurance charges and repair bills.

Increases in auto repair costs are running "10-15-20 percent" higher than a year ago said Jim Young, an actuary for Allstate, who noted that repair costs began climbing late last year after remaining relatively stable for many months.

"Everything we're seeing right now indicated very, very strong pressure toward higher costs," said Young. Allstate raised its Virginia rates by 13 percent earlier this year but has no plans to raise rates in the District or Maryland, he added.

State Farm reported its average Virginia auto repair claim was up 17.9 percent in the first quarter of this year compared to a year ago. Medical claims were up an average of 11.3 percent.

As a result, State Farm said it paid out $1.2 million more in claims than it collected in premiums in Virginia during January, February and March. The company announced a Virginia rate increase averaging 10.3 percent, but stressed the actual amount will vary depending on the type of car, and where and how it is driven. State Farm is not at present asking for higher rates in Maryland or the District.

Geico officials said they have not yet determined the amount of increase they will request in Maryland and have no rate increases pending in other local areas.

Nationally, Geico's claims are averaging about 15 percent larger than last year.

The auto insurance companies reported no increase in the frequency of their claims and held out the hope that gasoline shortages might mean less driving and fewer accidents.

That's what happened in the 1973-74 Arab oil embargo, but pent-up inflation socked the insurance companies with huge claims increases the following year and sent rates soaring.