In what is the nation's first plan to disposed of its nuclear garbage, President Carter will ask Congress today for permission to buy a permanent repository for radioactive waste and a storage pool for burned-out nuclear fuel.

The predisent will declare in a six-page message to Congress his intention to select by 1985 at least one permanent repository for radioactive wastes from among 11 candidate sites. They include the Nevada Test Site, where nuclear weapons are detonated underground, the Hanford, Wash., site, where military wastes are already stored, and eight underground salt domes inland from the Gulf of Mexico in Mississippi, Louisiana and Texas.

In an accompanying move, Carter will tell Congress he plans to scrap a controversial research program to bury military nuclear wastes in a salt mine in New Mexico. The cancellation of the Waste Isolation Pilot Plant comes after $90 million has been spent developing the site 30 miles southeast of Carlsbad.

"The site near Carlsbad will continue to be characterized and if qualified will be reserved along with [the 10] other sites for possible future use as a licensed repository," Carter will tell Congress. "It is important that we take time to compare the New Mexico site with other sites now under evaluation for the first waste repository."

The president will tell Congress he intends to establish a repository for burned-out nuclear fuel by 1983, declaring that he wants legislation by 1981 authorizing the federal government to buy at least one "away-from-reactor" storage site. This site would be used to keep burned-out nuclear fuel now accumulating at nuclear power plants around the United States.

There are three candidate sites for the away-from-reactor storage pool: Barnwell, S.C., Morris, Ill., and West Valley, N.Y. West Valley would need a $1 billion cleanup from past nuclear contamination before it could be reused.

Sources said that the Morris site could be bought for no more than $100 million, while the Barnwell site might cost as much as $350 million.

Spent nuclear fuel and radioactive wastes are not the same thing. Plutonium and other valuable isotopes are still locked up inside spent fuel and can be removed through reprocessing. The radioactive waste -- what remains after the plutonium is removed -- is what the federal government wants to bury permanently.

The nation's 70 operating nuclear power plants are running out of space to keep their spent fuel, which grows in volume every year. Most of the spent fuel is being kept in shielded swimming pools alongside the power plants. s

Once the away-from-reactor storage pool were built, spent nuclear fuel would be removed from operating power plants and trucked to the storage pool. Plant owners would pay the federal government storage fees. Carter will propose accepting spent foreign fuel as well as domestic fuel, to make sure plutonium is not diverted out of it to make nuclear weapons.

Barnwell and Morris started out as sites for reprocessing plants to extract plutonium from spent fuel. Early in his administration, President Carter ordered a ban on reprocessing, which put both sites' activity in a kind of limbo.

In his message to Congress, Carter will say he wants to select by 1985 at least one permanent burial ground for radioactive wastes. Carter said that exploratory drilling and excavation will begin immediately on the 11 candidate sites.

Sources said that shafts costing between $150 million and $200 million each will be sunk in the four or five better sites to determine which is best for radioactive waste burial. The better test sites are expected to include the Hanford Reservation in Washington and the Nevada Test Site near Jackass Flats, Nev.

Almost all the radioactive waste in the United States is spent military fuel that has been reprocessed to extract its plutonium since before 1950. About 100 million gallons of highly radioactive waste is stored in double-walled stainless steel tanks at Hanford and Savannah River, S.C., alongside the reprocessing plants.

Carter will tell Congress he will establish an advisory panel, the State Planning Council, to coordinate all aspects of the federal waste program with the states involved.

To his council, Carter said, he will appoint nine governors and five officials from the departments of Energy, Interior and Transportation and the Environmental Protection Agency and the Nuclear Regulatory Commission. One of the governors will be chairman.

One reason Carter is canceling the Carlsbad project, sources said, is that it was badly coordinated between federal and state agencies. Sources said the Carlsbad project was begun without consulting the Interior Department and the Nuclear Regulatory Commission and with little regard for New Mexico's objections to the project.

"We want to end that old way of doing things," one source said. "It's time to start anew."