The present study addresses a computational work of the weak shock wave propagating inside an automobile exhaust muffler. Several different types of the silencer systems are employed to investigate the magnitude of the shock wave during propagating through them. The Initial shock wave Mach number $M_s$ is varied between 1.01 and 1.30, and a normal shock wave is given at the inlet of the silencer systems. The second order total variation diminishing scheme Is employed to solve the two dimensional, compressible, unsteady Euler equations. The present computational results are compared with the previous experimental ones available. The present computations predict the experimental results with a quite good accuracy. Of the four silencer systems applied. the most desirable silencer system to reduce the peak pressure at the exalt of the exhaust pipe is discussed from the Point of view of the engineering design of the silencer systems.