At least part of the inner circumferential wall of the outer casing is provided with a concave surface opposing the rotor blade tips as seen in a longitudinal section. Typically, each of the rotor blades is provided with aerofoil section, and the compressor is designed as a transonic axial flow compressor. Thereby, a compressive wave is produced upstream of the shockwave so that the Mach number of the flow entering the shockwave can be reduced. As a result, the shockwave is made less severe, and the shockwave loss can be reduced. In particular, because the concave surface is provided in the casing wall as opposed to the case where the concave surface is provided in the negative pressure side of the rotor blade, the reduction in the performance owing to the change in the angle of the airflow entering the passage defined by the concave surface under a partial load condition can be avoided.