A cylinder sleeve assembly cast in a cylinder barrel assembly in a cylinder block for a multi-cylinder internal combustion engine, comprising a plurality of cylinder sleeves whose adjacent cylindrical peripheral walls are coupled to each other, a plurality of first sink mark inhibiting engaging portions provided in each valley-like area of an outer peripheral surface of the cylinder sleeve assembly which is located on opposite sides of a coupled portion between the adjacent cylindrical peripheral walls, said first sink mark inhibiting engaging portions being engaged with said cylinder barrel assembly during casting of said cylinder block, said first engaging portion being formed in such a manner that an engaging portion-bisecting division plane which intersects a curvature circle of the outer peripheral surface of the cylinder sleeve and extends in an axial direction of the cylinder sleeve, has a predetermined inclined angle inclined toward the coupled portion with respect to a reference plane which includes an intersection between said division plane and the curvature circle and the center of the curvature circle and extends in the axial direction of the cylinder sleeve, and a plurality of second sink mark inhibiting engaging portions provided in opposite end areas of the outer peripheral surface of the cylinder sleeve assembly in a direction of arrangement of the cylinder sleeves, said second sink mark inhibiting engaging portions being engaged with said cylinder barrel assembly during casting of said cylinder block.