The invention relates to a cylinder sleeve (2) for lining the cylindrical wall of a cylinder (A1) of an internal combustion engine. The inventive sleeve (2) comprises an inner wall (3) which is intended to guide a piston in translation and an outer wall (4) which is intended to rest on the cylindrical wall of the cylinder. The outer wall (4) of the sleeve of the cylinder (2) comprises an upper part (6) which is flared toward a top edge (5) of the sleeve (2), which is defined between the inner (3) and outer (4) walls of the cylinder sleeve. The invention also relates to a cylinder block of an internal combustion engine, comprising at least two cylinders (A1, B1) which are each equipped with one such cylinder sleeve.