PURPOSE: To eliminate the out of roundness to appear after machining a cylinder bore, by sealing up a pressure liquid in the cylinder jacket at the time of machining the cylinder bore so that a uniform pressure will exert on the backside of the cylinder bore to prevent production of strain in the cylinder bore due to the machining.

CONSTITUTION: A liquid W such as a coolant is supplied from a liquid supply pipe 11 to the water jacket 3 in a cylinder block 1 and the liquid is sealed up in the jacket 3 at a high pressure, whereby a uniform pressure by the liquid W is arranged to be exerting on the backside of the cylinder bore 2. In this condition, a honing shaft 14 is operated to hone the internal surface of the cylinder bore 2, when, since escaping of the cylinder bore 2 in the direction of its wall is suppressed by the pressure, the bore 2 is kept free from strain and the out of roundness of the cylinder bore 2 appearing after the machining can thus be eliminated.