President Carter sent a costly, complex gasoline rationing plan to Congress yesterday that is intended to be used only in case of a severe oil shortage. The plan would give the average motorist about 40 gallons monthly for each car owned.

Gasoline users would be free to buy ration coupons from other motorists. Department of Energy officials said the coupons would probably sell for from $2 to $5 per gallon of gas during a 20 percent shortfall lasting at least 30 days -- the minimum condition needed to trigger use of the plan.

While coupons would be distributed on the basis of motor vehicle registration, owners in states where gasoline use per vehicle has been above average would get additional coupons.

Energy Secretary Charles Duncan called the plan "the best we could devise," but emphasized it would be expensive -- about $2 billion a year -- and "enormously complicated."

Because of the cost, the complexity and the basis on which coupons would be distributed, some opposition to the plan is expected to Congress, which turned down the administration's last attempt, in 1979, to get a standby gasoline rationing plan approved.

As of yesterday, congressional sources said there was little organized opposition to the plan.

The administration was required by the Emergency Energy Conservation Act of 1979 to submit the plan, which Congress has 30 days to reject. Like the recent vote against Carter's proposed oil import fee, a rejection -- which would have to be by both houses -- could be vetoed by Carter.

DOE designed the plan along the lines dictated by the energy law, which required that it take past gasoline use into account in distributing ration coupons. DOE officials said they believe the plan meets most of the objections that caused the earlier proposal to be rejected.

The new system would work this way:

Individuals would be eligible for a ration allotment for each vehicle owned but with an yet unspecified limit on the number of allotments for each household. Ration checks would be sent by mail and would be exchanged at about 60,000 distribution points, such as banks, for ration coupons. The coupons would be required for all gasoline purchases.

Business would get allotments based upon vehicle ownership and supplemental allotments based on past use.

Some units of government and businesses providing essential services could get supplemental allotments.

Local rationing offices would handle special allotments for hardship applicants and handicapped individuals. Each state would have a coupon reserve, probably about 5 percent of its total allocation, for local offices to draw upon.

With 153 million motor vehicles registered in the United States, the monthly distribution of ration checks would dwarf the 35 million checks sent monthly by the Social Security Administration or the 21 million foodstamp distributions each month.

Use of rationing "would involve, in effect, creating a entirely new currency," a DOE report to Congress said.

With a 20 percent shortfall in oil supplies, "the ration rights distributed each quarter would be worth roughly $40 billion," it said. About $110 billion worth of currency and coins is now in circulation in the United States.

The actual average allotment would depend on the shortage. Using 1978 gasoline consumption figures, with the allotments for various priority users and state reserves taken off the top, DOE estimated that a 20 percent shortfall would require cutting the average motorist's monthly gas use per vehicle from 60 to 42 gallons.

Since current gasoline users is well below that of 1978, a 20 percent shortage probably would leave the average motorist with less gas than that.

The plan would assign a motorcycle one-quarter the gasoline ration of an automobile, and a moped one-tenth of an automobile ration.

The DOE report said that on the basis of 1977 data, households with incomes of $10,000 or less would, on average, gain from the plan because they use less than 40 gallons of gas a month in their vehicles. Households with incomes between $20,000 and $30,000 would need to buy the most additional coupons, it said.