LAS VEGAS, Nev. (AP) _ Nevada's largest labor union set up picket lines Tuesday at the nation's nuclear testing grounds and at a desert range where Stealth aircraft are based, and more than 2,000 workers honored the lines.

Jim Arnold, head of the powerful Culinary Union Local 226, said earlier this month his organization could shut down the facilities in the desert northwest of Las Vegas.

Super-secret Stealth aircraft use the Tonopah Test Range, a desert air base 200 miles northwest of Las Vegas. Nuclear weapons testing and some ''Star Wars'' research is carried out at the Nevada Test Site, 65 miles northwest of the city.

Energy Department officials say the strike could delay projects at the two sites if it continues.

The pickets went up at 3 a.m. after talks broke down. The union is seeking increased wages and benefits from Reynolds Electrical and Engineering Co., the major contractor at the sites.

The Culinary pickets joined bus drivers who struck the Las Vegas-Tonopah- Reno Stage Lines Inc. on Aug. 15. The buses, which normally carry some 3,000 workers to the test site daily, have continued to run with substitute drivers.

Reynolds spokesman Steve Leon said the company had 2,971 union employees scheduled to report to work at the two sites Tuesday and 2,761 failed to show up.

As many as 2,000 union employees have failed to report to work at the test site on various days the past two weeks, refusing to cross the lines of the 121 striking bus drivers.

The union members include steelworkers, mineworkers, laborers and others. They are used primarily for drilling vertical shafts and working mines in which nuclear weapons tests are conducted.

The 617 Culinary workers employed by Reynolds provide food services for some 8,300 workers at the test site.

More talks are scheduled between the two sides Wednesday and company officials say they plan some counter proposals.

The Culinary Union had been threatening to strike since its three-year contract with the company expired Aug. 4.

They have been seeking a $1-an-hour across the board pay increase this year, 3 percent raises each of the next two years and increased benefits for the health and welfare fund. The company has countered with a wage freeze this year, a 2.2 percent pay increase next year and 3.2 percent increase in 1989.

Leon said Culinary workers now earn from $8.65 to $11.27 an hour.

The last major strike at the test site was in 1970. The government was able to continue its testing program at that time.