A flow machine for a fluid is presented with a radial sealing gap (9) between stator parts (4) and a rotor (3), wherein at least one wear ring (5) is provided at the sealing gap and is fastened to a stator part (4) via an elastically deformable fastening part. The fastening part (6) is connected on the one side to the stator part (4). On this side a radial gap (8) is formed between an outer jacket surface of the wear ring and the fastening part and, on the other side, with the wear ring. On this side a radial gap (7) is formed between an outer jacket surface of the fastening part and the stator part.