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The group sent a letter to a radio station in Berkeley, California, saying it was holding Miss Hearst in "protective custody".
The letter included a petrol credit card issued to Miss Hearst's father, Randolph Hearst, president of the San Francisco Examiner newspaper.
Miss Hearst stands to inherit the vast Hearst publishing empire, founded by her grandfather, the flamboyant media tycoon, William Randolph Hearst.
The letter went on to say it was "an arrest warrant issued by the Court of the People," and ransom demands would be made in later communications.
It warned that Miss Hearst would be executed "should any attempt be made by authorities to rescue the prisoner".
The SLA is a shadowy, violent underground organisation with radical political views.
It emerged for the first time only last November, when it said it had carried out the murder of the popular black school administrator, Marcus Foster.
He was shot dead, and a colleague wounded, as he left his school in Oakland, California.
Patricia Hearst was taken from her flat in Berkeley two days ago, by a group of two men and a woman. Her fiancé, Steven Weed, and a neighbour, Peter Benenson, were badly beaten in the struggle.
Police helicopters have been searching the hills near the University of California for the white estate car which they believe was used in her kidnapping.
Police now say they suspect at least five people, including two women, were involved in the kidnapping, after evidence from the owner of one of the two getaway cars. He was left bound and blindfolded in a back seat after the car was abandoned.
Miss Hearst's parents issued a plea to the kidnappers in a statement yesterday, saying, "At this point, their only crime is abduction. For their sake and ours, and especially for Patricia, we plead with them not to make it any worse."
The SLA held Patty Hearst hooded and tied up in a cupboard.
Over the following weeks, the group apparently brainwashed her into accepting their ideas, until in April 1974 she was caught on closed circuit television helping them to rob a bank.
She went on the run, but was caught by the FBI. After a sensational trial, she was sentenced to seven years' imprisonment, but was released after three years. She was pardoned in January 2001 by President Clinton.
Hearst married her police bodyguard, Bernard Shaw, and now lives in Connecticut with two daughters.
The SLA is thought to have only ever had about 12 members. Six, including the group's leader, Donald DeFreeze, were killed in a police shootout two months after the kidnapping.
The remaining five members lived quietly under assumed names for over 20 years, until the FBI tracked them down.
The last SLA fugitive, James Kilgore, was arrested in Cape Town in South Africa in 2002. All are now in jail.
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