HOLLYWOOD, Aug. 9— Jello Biafra, the founder and lead singer of the Dead Kennedys rock band, goes on trial Monday on charges of violating a California statute that makes it illegal to distribute, exhibit or send harmful material to a minor.
The misdemeanor charge stems from a poster in the band's 1985 album, ''Frankenchrist.'' A reproduction of a painting by H. R. Giger, a Swiss surrealist, the poster showed 10 sets of male and female genitalia. Charges were brought in June 1986, after a California woman, Mary Sierra, sent the poster to the California Attorney General's office with a complaint that her daughter, who was 14 years old, had bought the record.
A Los Angeles Deputy City Attorney, Michael Guarino, said the case against Mr. Biafra, as the owner of the record company Alternative Tentacles, and four other distributors of the record was intended to test ''where the lines ought to be drawn'' in the availability of sexually explicit material to minors. New York Case Cited
He said the California statute under which Mr. Biafra is being prosecuted followed a decision by the Supreme Court of the United States in the case of New York v. Ginsburg over the sale of a men's magazine to a minor. In that case, the court held that the state had a compelling interest in the protection of children in matters that would not be obscene in regard to adults.
Violation of the California statute is a misdemeanor punishable by a year in jail and a $2,000 fine, but Mr. Guarino said it was highly unlikely he would ask for anything but a suspended fine if he won the case.
An American Civil Liberties Union lawyer, Carol Sobel, who is one of Mr. Biafra's attorneys, said, ''You don't have to like the painting, but if everybody agrees the material is O.K. for adults to have, it's inconsistent to criminalize it because it was bought by a minor.''
Mr. Biafra's chief lawyer, Philip Schnayerson, said the prosecution of Mr. Biafra was an attempt to set a precedent in liability. ''Traditionally, you don't prosecute the beer manufacturer because a bartender sells to a minor,'' he said. ''Mr. Biafra and the record companies had no control over who the record was going to be sold to.''
Mr. Biafra said the Dead Kennedys had been chosen for prosecution rather than more prominent rock artists because they had fewer monetary resources and because their records make political points. He said Mr. Giger's poster was included because it heightened the record's subject matter: ''The vicious circle we find ourselves caught in when we exploit each other in today's me-generation consumer culture.'' Warning Labels on Records
Under pressure from Parents Music Resource Center, a group formed by Tipper Gore, wife of Senator Albert Gore Jr., a Tennessee Democrat, the major record companies have agreed to put warning labels on records that contain visual material or lyrics that might be harmful to minors. Mr. Biafra described ''Frankenchrist'' this way: ''The inside foldout to this record cover is a work of art by H. R. Giger that some people may find shocking, repulsive, or offensive. Life can sometimes be that way.''
The Dead Kennedys, who disbanded last spring under the pressure of the court case, were a politically oriented San Francisco-based punk band best known for their songs ''Holiday in Cambodia'' and ''California Uber Alles.'' The Los Angeles Times described their final album, ''Bedtime For Democracy,'' as their ''usual exhilarating blast of politically oriented thrash punk'' and Mr. Biafra, whose real name is Eric Boucher, as ''one of rock's intelligent spokesmen.'' Among the subjects of Mr. Biafra's songs on ''Bedtime for Democracy'' are toxic waste and United States immigration policy, while the cover of ''In God We Trust,'' an album that attacked the religious right, depicts Christ, crucified on a cross of dollar bills, as a bowling trophy.
A friend of Mr. Biafra, Suzanne Stefanac, a co-founder of his defense fund, said $30,000 had been collected ''from fans of the Dead Kennedys and people concerned with censorship.''
Mr. Biafra said, ''The punishment has already been meted out very severely because I've had a year of my life completely disrupted and I've been unable to perform any more music.'' Recently he has spoken his lyrics in clubs and at universities, including the University of California campuses at Los Angeles and Santa Barbara.
Mr. Giger shared an Academy Award for visual effects in 1979 for his creation of the aliens and their disturbing environment in the movie ''Alien.'' The painting on which the posters were based has been exhibited in European museums. August 10, 1987)