A method for performing a filleting cut for filleting fish which are conveyed tail-first is carried out along a row of wedge-shaped ray bones projecting away from a main bone stem with a wedge width increasing from ray bone to ray bone by a pair of circular knives having sharp cutting edges. Starting from the tail end, meat of each fish is cut by the circular knife pair having a V-shaped arrangement as a result of the fact that a cutting gap having the smallest cutting edge spacing is set to a basic size which is at least substantially equal to or smaller than a wedge width of the outermost ray bone at the tail end of the conveyed fish. In the fixed position of the V-shaped arrangement, the ray bones are guided through the cutting gap, wherein the circular knife cutting edges, which in their cutting edge region are flexibly deformable out of the associated circular knife surface counter to an elastic restoring force, are displaced counter to the elastic restoring force by the broadening ray bones with increasing widening of the cutting gap. A tailored suitable apparatus comprises a circular knife pair having cutting edges which, in the fixed V-shaped arrangement, are designed such as to be able to be deformed with a degree of deformation defined by the difference between ray bone wedge widths. Circular knives configured for the apparatus may each have a cutting edge region which is deformable in a wave-like manner along the cutting edge as a result of a bending pressure transverse to the circular knife surface.