PURPOSE: To finish the inner cylindrical surface of a liner or a sleeve precisely for minimizing abrasion to a manufacturing tool by boring the liner or the sleeve precisely, and housing them closely in a cylindrical bore in a cylinder block portion after a honing process.

CONSTITUTION: In manufacturing an engine block assembly, an integral cylinder head 25 having a cylindrical bore 13 with a cylinder head surface 27 at the inner end 21 and a cylinder block member 19 are manufactured. After a sleeve 11 having the inner cylindrical surface and the inner end 33 is manufactured, the major portion of the sleeve 11 is inserted into the cylindrical bore 13 leaving part of the sleeve 11 so that the inner end 33 of the sleeve 11 may be separated from the cylinder head surface 27. After the inner cylindrical surface of the sleeve 11 is bored, the sleeve 11 is fully inserted into the cylindrical bore 13 so that the inner end 33 of the sleeve 11 may engage with the cylinder head surface 27, thereby completing the engine block assembly.