A pair of swimsuit models are out in a boat to stage a publicity stunt by appearing to be stranded. They discover a mysterious galleon shrouded in mist and board it. When contact is lost, the wealthy and unscrupulous businessman who sent them out decides to mount his own rescue mission and abducts one of the models' friends. The abducted girl makes an unsuccessful escape attempt. The businessman and his secretary recruit an eccentric scholar to assist them in their search for the missing models and their boat.