an exhaust muffler for an internal combustion engine including an outer shell containing two halves made of synthetic resin material , a metallic inner pipe extending through the parting plane between the two halves via a tubular extension extending integrally from the two halves , and an outer sleeve which is fitted onto the tubular extension , preferably by using a bayonet mount structure , for securely joining the two halves at its one end and forming an air - tight seal in cooperation with the part of the inner pipe extending out of the tubular extension at its other end . an arrangement is provided for accommodating a relative displacement between the other end of the outer sleeve and the inner pipe for avoiding the generation of thermal stress due to the difference in the coefficient of thermal expansion between the outer shell and the inner pipe made of different materials .