Alexandria Police Chief Charles T. Strobel, whose 240-man department has been troubled by low morale and criticized for its handling of several criminal investigations, was named yesterday as one of nine nationwide finalists for a job as Florida's chief law enforcement official.

Strobel, 42, is one of three Washington area residents under consideration by the Florida Department of Law Enforcement to head the statewide criminal investigation agency.

Perry A. Rivkind, a law enforcement administrator with the Justice Department, and Lloyd A. Bastian of Reston also were named as finalists for the $35,500-a-year post.

Rivkind, 47, who said he has "trained half the police in this country," yesterday called Florida department's selection process "demeaning."

"It's unusual, to say the least," he said. "They've invited us down to Tampa for a cocktail party and dinner. I think it's childish." Rivkind said he would not be in the running for the job. "I don't drink," he said.

Bastian could not be reached for comment.

Strobel, said he would "most likely" go to Tampa May 18-19 for the interview and called the job prospect "an opportunity."

Strobel, a 21-year veteran of the Alexandria force, was named chief two years ago. Since then his department has come under fire for its handling of some undercover narcotics and vice investigations, including the use of a civilian volunteer last year in a probe of the city's massage parlors.

"If I live to be 110," Strobel said yesterday, "I'll never do that again."

Earlier this year, the department was accused of covering up a key police report involving sexual bribery allegations against former chief prosecutor William L. Cowhig, which Cowhig has denied. One top police official resigned after a departmental investigation, admitting his role in the coverup.

The force also has been criticized for its handling of the 1978 murder of Old Town socialite Donita Cutts, which is still unsolved.

"There have been ups and downs," Strobel said yesterday, adding that he has not yet made "a firm decision" on whether to leave his $36,500-a-year post.