Picture a small missile at the bottom of the sea and carrying a payload of high-level nuclear waste. Its mission, should the nation choose to accept it, would be to bury the material forever hundreds of feet below the ocean bottom by hitting the mud at 120 miles per hour.

The Department of Energy is spending $5.9 million this year to study the idea, with outlays increasing to $15 million in 1984. Although any tests are at least 20 years away, critics are saying it is not too early to get worried.

Proponents counter that the waste has to go somewhere, and that the deep seabed offers some of the most stable, ancient and otherwise useless burial sites on earth.

Defense programs and the nuclear power industry have been piling up wastes slowly for 30 years in temporary storage areas, awaiting a decision on permanent disposal.

There are about 80 million gallons of high-level defense wastes in storage, much of it in leaky containers buried near Hanford, Wash. Some 12,000 tons of spent nuclear fuel rods await the future in "swimming pool" storage tanks that are rapidly filling up at power plants nationwide.

The wastes remain dangerous for thousands of years. When President Carter outlined his 10-year study and testing plan for a site decision in February, he called seabed burial one of the "long-range options" to his primary choice of onshore entombment in some geologically stable drilled pit.

But environmental or technical verdicts on any land-based site may be negative in the long run. Even when one is chosen, there is no assurance that local reaction to it will be joyful.DOE wants to have an alternative ready.

"This program doesn't have the urgency to it right now of some others," said Wendell Webber, oceans specialist at the Environmental Protection Agency, "but it's important to be able to answer the questions when the political pressure does come to bear."

In the most popular vision of seabed emplacement, wastes solidified into glass and cased in stainless steel and concrete, would be loaded into missile-shaped canisters about 12 feet long and one foot across. These would be expected to endure about 500 years, the period of greatest heat and radioactivity. Each projectile could hold the equivalent of one spent fuel assembly from a nuclear power plant.

The containers would be taken on specially equipped ships to carefully chosen sites near the center of the great tectonic plates that form the earth's surface, well away from any volcanic or geologic activity. They would then be dropped overboard, hitting the sea bottom two to three miles down at an estimated 120 miles per hour.

Alternatively, they could be lowered by cable to within 130 feet or so of the bottom and still hit the mud at that speed. Weighing 1,500 to 3,000 pounds each, the canisters would bury themselves 100 to 300 feet deep in bottom sediments, which have been described as having the consistency of stiff chocolate pudding.

D. Glenn Boyer, seabed project manager of DOE's waste isolation division, said the muck would close over the missiles "like shooting a bullet into a bucket of mud." Complex monitoring devices would be set on the bottom nearby and if any leakage were detected, the canisters could be retrieved for repackaging with existing drill technology, he said.

"We're not really proponents of this concept, but we feel obligated to look at the best geological formations we can find, and many of them lie underneath the oceans," Boyer said.

The gravity-drilling technique is used now by the oil industry to put seismic detection equipment and offshore drilling rig anchors into the ocean bottom, Boyer said. However, many other technical and nearly all the political questions hae not been addressed, much less answered, he said.

Among these are issues of transport requirements, monitoring time needs, port and shipping facilities and jurisdiction over the sites, which will be in international waters. The so-called Ocean Dumping Treaty of 1972, ratified by the United States, prohibits dumping high-level nuclear wastes into the water but is silent on the question of wastes below the seabed.

Much more research is planned into the interaction of ocean pressures and deep-sediment processes with heat, which would be about 200 degrees Centigrade on the outside of the canisters. Does any of the fish we eat feed at the three-mile depths? If so, what changes might a leaky canister mean to them in a few hundred years? Little is known about deep-sea lifestyles. "We haven't even defined the term 'innocuous impact'," EPA's Webber said.

Although DOE's most optimistic estimates see a test drop by the year 2000 at the earliest, the Oceanic Society is worried that the idea has been gathering steam with virtually no public attention.

"There is a strong movement by a commercial interested community to find a politically easy choice for nuclear waste management," said Christopher Roosevelt, president of the 65,000-member marine policy study organization. By that, he said, he meant defense industries, public utilities and nuclear suppliers committed to a nuclear future.

"As always, it's the oceans that get looked at. Fish don't vote," Roosevelt said. He said there should be more emphasis on the problems of monitoring the sites, transport to them and retrieval of damaged canisters. "We have got to have a lot more public discussion of this whole thing before it goes a lot further," he said.