The Energy Department yesterday picked sites in Texas, Nevada and Washington state as the leading candidates to be the nation's first permanent burial ground for nuclear waste but immediately encountered legal and political opposition.

Nuclear reactors across the country are rapidly running out of temporary storage space for their growing volume of spent fuel, which has now reached 70,000 metric tons.

Energy Secretary Donald P. Hodel said the government plans to begin placing the waste, which will remain radioactive for thousands of years, in a permanent storage site in 1998.

The three prime sites are Deaf Smith County in the Texas Panhandle, Yucca Mountain in Nevada, about 100 miles northwest of Las Vegas, and the government's Hanford Works reservation northwest of Richland, Wash.

Selected as backup sites were Davis Canyon, just outside Canyonlands National Park in Utah, and Richton Dome, a salt dome near Richton, Miss.

President Reagan will pick three of the sites next summer for extensive drilling and testing. When the permanent site is chosen in about 1990, the governor or legislature of that state can veto the selection, but Congress can override the state.

The torrent of criticism from environmentalists and state and local officials underscored the fact that nuclear waste is a problem that most people want buried in someone else's backyard.

One positive comment came from Mayor John Poyner of Richland who said selection of the Hanford Works reservation would be "a real shot in the arm for the city of Richland . . . . We have been looking forward to this, and it is a real positive step for us."

But most reaction was negative.

Texas Attorney General Jim Mattox filed suit to block establishing a site in his state even before the formal announcement yesterday.

He said the Energy Department's proposed burial site in Deaf Smith County, about 30 miles west of Amarillo, is prime farm land that contains the drinking-water supply for parts of several states.

"It's some of the best farm land in the country," said Elna Christopher, a spokesman for Mattox. "There are better places to put it than there. It just makes no sense."

Critics said studies by the Nuclear Regulatory Commission, U.S. Geological Survey and others show that the Hanford site sits on fragile volcanic rock formations that are subject to considerable horizontal stress.

"Hanford may be the worst of all possible sites," said Sierra Club lobbyist Brooks Yeager.

Washington governor-elect Booth Gardner said he was worried about "possible groundwater contamination" at the site, which is near the Columbia River.

Critics said that Yucca Mountain, which is near Nellis Air Force Base, also sits on volcanic rock and is subject to "mini-earthquakes" from ground vibrations at a nearby nuclear test site.

The Wilderness Society said the selection of Davis Canyon as a backup site would violate "the fundamental integrity . . . of our national parks."

Hodel disputed much of the environmental criticism, saying the recommendations were based on careful studies and public hearings.

"Right now, I think we'd have to say that none of the states is supportive," Hodel conceded. But he said he hoped that would change as more research is done.

The Sierra Club, the Environmental Policy Center and the National Parks and Conservation Association filed suit Tuesday to block the selection process.

Yeager called the proposed sites "a basketful of lemons. They really weren't chosen through a methodical process . . . . The department has committed itself to a schedule that's basically impossible to meet."

Texas officials said there was no way that nuclear waste could be buried in Deaf Smith County without disturbing the underground aquifer that provides drinking water and irrigates the region's farm land. Their suit also focuses on DOE's procedures.

"We contend that they violated their own rules and regulations," Christopher said. "They decided Texas was going to be the place, so they were writing their regulations to fit that."

Rep. Harry M. Reid (D-Nev.) said he and Gov. Richard Bryan strongly oppose the Yucca Mountain site.

"I don't think we can have a nuclear dump that's compatible with the tourist economy," Reid said.