A doomsday version of an umbrella is being developed in hopes it could stop enemy nuclear warheads while they are still 300 miles above the United States.

Maj. Gen. Grayson D. Tate Jr., head of the Army's missile defense command at Huntsville, Ala., said last week that the flying umbrella "holds great promise." Lockheed is getting $188 million to build one for flight testing.

The umbrella project is fresh proof that the search for a missle to stop a missile goes on, despite the death of the anit-ballistic-missile defense President Johnson started to put around the United States in the 1960s.

"For the sake of the country," Tate told reporters at a breakfast, "we have got to continue with a very vigorous ballistic defense to preserve options."

The United States and the Soviet Union have for the moment decided to leave their populations naked to nuclear missile attack. The existing anti-ballistic missile treaty allows experimentation, but not extensive deployment of advanced missile defenses.

The flying umbrella is part of the experimentation allowed under the treaty. Tate gave a glimpse of how the highly secret device would work, adding that its first flight test will be conducted in about two years from the Pacific Island of Kwajalein.

The Minuteman rocket for hurling nuclear warheads at the Soviet Union in a war will carry the umbrella into space in its upcoming flight test. A second rocket will give the umbrella the thrust to poke around the outer reaches of space.

On the way up into space, the umbrella would be folded. But once in the target area, it would unfurl itself to a diameter of about 15 feet.

Its killing quality, Tate said, would come from the fist-sized weights strung out along the ribs of the umbrella. The umbrella would pack no explosive devices.

Instead, once the umbrella's sensors detected the incoming warheads, the whole gangly rig would be propelled toward them, colliding with several warheads at once, it is hoped. The high-speed collision, Tate said, would knock the warheads to smithereens.

With no wind resistance to slow it down in the vacuum of outer space 300 miles above the earth, Tate said the umbrella would hit its targets while traveling 30,000 feet per second.

The Pentagon calls the umbrella the Homing Overlay Experiment, or HOE.

The same kind of Strangelovian collision is seen by the Pentagon as one way to destroy Soviet satellites, if war should ever move to outer space. Experiments are under way with a "flying tomato can" that would home in on the heat of an enemy satellite and ram right through it.

The flying umbrella, Tate said, "holds great promise" for combating "relatively cheaply" the showers of warheads the Soviets could launch if doomsday ever came. "It puts leverage back in our pocket."