Alexandria Democrats nominated former City Council member Beverly Beidler yesterday to run for state senator this fall against the incumbent, two-term Republican Wiley F. Mitchell Jr.

Beidler defeated Jared Cameron, a travel agency owner, 559-to-212 at the Democrats' three-hour mass meeting to choose a nominee for the race in the 30th Senatorial District, which covers all of Alexandria and eight precincts in Fairfax County.

If elected to a four-year term in November,Beidler said she would continue her efforts to make voter registration more accessible and focus on such issues as land use, water quality, health-care costs, transportation, education, housing, job retraining and fair treatment for women, minorities, tenants and working people.

In a speech that was critical of the Reagan administration and laudatory of that of Virginia Gov. Charles S. Robb, Beidler said, "I have established a record of taking time to examine problems first hand, giving a fair hearing to all sides, and carrying out campaign promises."

Beidler, 54, was a member of the City Council from 1973 to 1979, where she was an outspoken advocate of Metro service to Alexandria and an opponent of I-66.

She gained a reputation for her sharp questions, her concern for minorities and her grasp of complex issues.

For the last four years, she worked for the U.S. Department of Housing and Urban Development as an adviser to state and local governments on ways to improve their management and delivery of public services. She resigned in March to pursue the State Senate job since federal employes are barred by the Hatch Act from participating in party politics.

Mitchell, who could not be reached yesterday, was a three-term City Council member and vice mayor before he ran for the Senate in 1975. A lawyer, he was unopposed in his 1975 reelection bid and has a popular following in the city.

Donald Henry, chairman of the Alexandria Democratic Committee, said he believes Mitchell can be beaten this year. "He hasn't run for election in eight years, he hasn't been tested."