Mike Love and Brian Wilson have not commented on the suit, only the latest in a series of lawsuits which have divided the group for years.
"Jardine claims he has been frozen out of the Beach Boys," his lawyer Jeffrey Benice said.
Jardine, 58, has also claimed that he has had problems booking shows for his own project, the "Beach Boys Family and Friends" group.
The suit, for some $4m (£2.8m), was filed against Mike Love, Brian Wilson, the Carl Wilson Trust and Brother Records Incorporated in a New York Superior Court on 29 June.
Lawsuits
Jardine has complained that Love is promoting the current Beach Boys line up as the "real" and "genuine" group when, according to Jardine, Love is the only original member.
Mike Love and Brian Wilson have not commented on the suit, only the latest in a series of lawsuits which have divided the group for years.
In 1997 Jardine and Carl Wilson decided to take action against Brian Wilson for statements made in his autobiography.
But Carl Wilson was already suffering from cancer and died in February 1998.
In 1998 a US judge temporarily barred Jardine from performing under the name "Beach Boys Family and Friends" after representations from Mike Love and Brother Records.
Bassist and guitarist Jardine joined the Beach Boys before their first recording on the recommendation of Murray Wilson, father of Brian, Carl and Dennis.
He also wrote songs and provided the group with one of their last UK hits, Lady Lynda in 1979.
Meanwhile, Beach Boys co-founder Brian Wilson has admitted to struggling with mental illness and hallucinations that plague him on stage.
Speaking on American TV network ABC on Tuesday, he said: "I'm thinking, 'God help me if I get these crazy thoughts in my head,' you know.
"I have auditory hallucinations that I get.
"Voices saying, 'I'm going to hurt you, we're going to kill you', you know, crazy stuff."
At 59, Wilson said he will always be on medication to treat his condition - but he still wants to make music.
The songwriter was honoured with "An All-Star Tribute to Brian Wilson" on American TV on Wednesday - featuring Ricky Martin, Carly Simon, Vince Gill, the Go-Gos and Billy Joel.