Two attorneys employed by the Education Department's Office for Civil Rights sued the Reagan administration yesterday in U.S. District Court here, alleging that they were denied promotions because they refused to submit to security checks of their backgrounds and loyalty.

Kathleen Flake and William A. Delaney III, both senior trial attorneys, charged that their promotions from GS-13 to GS-14 have been shelved illegally by Education Department officials. The two lawyers contend that the action was taken because they resisted the security investigations, which apply to positions deemed "critical-sensitive" by the department.

The complaint, which has the support of the American Civil Liberties Union, termed the security-clearance requirement a "severe and unjustified invasion of personal privacy."

The security measures are part of a four-year-old administration campaign to expand the number of employes to be covered in several federal agencies. According to the complaint, the program was delayed last year after it drew criticism on Capitol Hill, but attempts to implement it resumed earlier this year.

A spokesman said the Education Department had no comment.

Lawyers in the Office for Civil Rights said last year that they suspected that the security crackdown might be an attempt to identify government employes who had leaked information that was critical of the Reagan administration's civil rights policies.

"This goes far beyond the regular check of records to see if you're a wanted felon," Arthur B. Spitzer, an ACLU attorney, said yesterday. "Presumably 'loyalty' is not supposed to mean 'political loyalty,' but whether you're a spy."

Spitzer said the ACLU is concerned that the investigations could be expanded to include "political flakiness" in the eyes of the administration.

Under security rules drawn for several agencies by the Office of Personnel Management, applicants for "critical-sensitive" positions must undergo not only a routine background check but also a full field investigation of "character, habits, morals, associations and reputation . . . ."

"Loyalty should be particularly stressed," the rules say. A 1982 Education Department directive said employment of "critical-sensitive" personnel must be "in the national interest and consistent with national security."

In their complaint, Flake and Delaney said that as government civil rights lawyers they "never have performed tasks capable of affecting the national security of the United States . . . . The Office for Civil Rights does not deal with issues related to the national security."

The two lawyers said they applied for promotion to GS-14 in May. According to the complaint, Flake was told in August that her application would not be processed until she completed the necessary forms for a full field investigation of her background.

Delaney later received the same notice, the court papers said. Both lawyers refused.

Named as defendants in the lawsuit are Education Secretary T.H. Bell and OPM Director Donald J. Devine, the Education Department, the Office of Personnel Management, Assistant Education Secretary for Civil Rights Harry M. Singleton and James B. Thomas Jr., the department's inspector general.