The invention relates to an L-shaped supporting body for accommodating a fish and for conveying said fish tail first through a cutting unit having a circular blade pair of a fish processing apparatus, which has a continuously revolving conveyor, wherein the supporting body has a main body for fastening said supporting body to the conveyor and a bearing web, which protrudes beyond a side wall of the main body and which has a supporting edge arranged at the top for accommodating the backbone of the fish to be accommodated, the bearing web having a groove arranged on the underside, which groove is designed as a counter-support for the circular blade pair. In addition, the invention relates to a corresponding apparatus for processing fish.