The suit, filed at a federal court in Manhattan, claims Sony has failed to live up to a contract requiring that it pay its musicians half of the net revenue it receives from licensing songs to download services like iTunes and Napster.
Sony has been paying the aging rockers less than that amount, in part because their record deals predate the existence of legal music sales over the Internet.
According to the suit, the record company is treating digital downloads like traditional record sales, rather than licensed music, triggering a different royalty deal.
Under that old rubrik, the record company deducts fees for the kind of extra costs they used to incur when records were pressed on vinyl, including packaging charges, restocking costs and losses due to breakage.
Tracks sold over the Internet usually go for about 99 cents. About 70 cents of the sale price goes to Sony.
The bands are getting about 4½ cents per song, according to the suit, rather than the approximately 30 cents they claim is rightfully theirs.
"I feel strongly that the record company is doing the wrong thing," said Brian Caplan, an attorney for the bands.
A spokesman for Sony BMG did not immediately respond to inquiries about the lawsuit.
The bands are seeking to have the suit declared a class action, which would cover all Sony artists who signed deals between 1962 and 2002.
The Allman Brothers Band signed its current Sony deal in 1989. Cheap Trick's deal dates to 1976.
While the amount of money at stake per song is small, it could add up to millions of dollars for Sony if a court rules for the bands.
Caplan estimated that there may be 2,500 recording artists covered by the class.
Sony Music is part of Sony BMG, a joint venture of Sony Corp. (SNE) and Germany's Bertelsmann AG.