The City of Alexandria, which will lose its police chief to retirement in December, has suffered a setback in its search for a replacement: Not many people want the job.

When the deadline for submitting applications passed earlier this month, 18 people had expressed interest in becoming chief, according to Assistant City Manager J. Thomas Brannan. He said city officials were disappointed by the relatively few candidates.

To increase the field, the city has extended the period for filing applications at least through this week and possibly until the end of the month. Brannan said the delay could make it difficult for the city to have the new chief in place before Charles T. Strobel leaves the post.

"We have already heard from some excellent, well-qualified people who could fill the job," Brannan said. "Our concern is the quantity of the candidates, not the quality. We just want to give an opportunity to people who may not have heard about the job before the deadline.

"We think we can keep the process open {through mid-August} and probably meet our goal of having a new chief by December," he said. "But if we elect to extend longer, that may be pushing it."

Strobel, who was the subject of withering criticism and a prolonged investigation during 1985 and 1986, announced in March that he would step down Dec. 3, the first day he is eligible for retirement.

In 1985, Strobel was accused of short-circuiting a drug investigation within his department, but he was not indicted by a grand jury. The next year he was charged with lying to that grand jury but was found not guilty.

Critics charge that the lingering allegations crippled Strobel's ability to manage his department. Strobel also has had strained relations with City Manager Vola Lawson, his immediate superior. Lawson will choose Strobel's successor.

City officials have said that all applicants for the job except those from within the Alexandria Police Department must have a minimum of five years' experience as police chief in a city of at least 75,000 people. Brannon said three of the 18 applicants came from within the city and the rest came from as far away as Colorado.

The salary range for the job is $56,000 to $62,000 a year. Strobel's annual pay is $76,000.