PURPOSE: To support an exhaust part from a car body without generating noise and the occurrence of a problem on heat resistance of rubber.

CONSTITUTION: In structure wherein an exhaust part, such as a muffler 6, is supported from a car body 5 through a resilient member, such as support rubber 3, support rubber 3 is arranged in the longitudinal direction of an exhaust pipe, the two ends of the support rubber 3 are supported to the car body 5, and a suspension support 12 fixed to the exhaust part 6 is caused to span the outer periphery of the intermediate part of the support rubber 3. The suspension support 12 is extended throughout the overall length of the exhaust part 6, the two ends thereof are fixed to the exhaust part 6, and the support rubber 3 is caused to span the central part of the suspension support.