The invention relates to an apparatus for cutting free the flank bones of decapitated, slaughtered fish with opened abdominal cavities which are transported on transport saddles as supporting bodies for securely receiving the fish in their abdominal cavities, comprising an upper bones guide, a lower bones guide and a separating assembly for releasing fish fillets from the flank bones, wherein the separating assembly, which can be brought from a standby position into a working position and vice versa, comprises a separating device having cutting edges and with a corresponding counter-surface, which is characterized in that a covering element, for covering regions of the cutting edge of the separating device located in the effective region of the separating device inside the fish, is assigned to the separating device, and the covering element is designed and configured such that it can be automatically adjusted with respect to its position in relation to the separating device. The invention further relates to a filleting machine with such an apparatus.