An arrangement (30, 80) for sealing a shaft (40, 60, 90, 110) in a casing (31, 81) by a hydraulic seal (50, 70, 100, 120) includes at least one essentially annular, radially inwardly open cavity (51, 71, 101, 121) and at least one essentially annular, radially outwardly directed sealing element (54, 74, 102, 122) which projects into the cavity (51, 71, 101, 121). To provide a hydraulic shaft seal, in which swirl and friction losses in the sealing medium are low and no leakage occurs, the hydraulic seal (50, 70, 100, 120) is arranged on the inner side (42, 62, 92) or on the outer side (111) of the shaft (40, 60, 90, 110) and the cavity (51, 71, 101, 121) or the sealing element (54, 74, 102, 122) of the hydraulic seal (50, 70, 100, 120) is connected to a wall (32, 82) of the casing (31, 81).