For preventing fatigue failures caused by the vibration stresses in a moving vehicle or an operating machine, it is important to clarify and predict dynamic response behaviors. Assuming a rigid installation, the vibration transmissibility of a double catalyst muffler system mounting on a table was examined through a vibration machine. Based on the measured data and by systematically taking vibration theories into consideration, a new prediction method of the vibration modes and parameters was proposed that takes account of vibration coupling and damping. A lumped vibration model with the eight-element and two mass points was set up, and the vibration response parameters were analyzed accurately from simultaneous equations of motion. In the vibration test, resonance peaks from the mounting table and muffler parts of two units were confirmed in three excitation drives. The first resonance peaks caused by the mounting table had lower frequency, but the vibration magnitudes from other parts at higher frequency were damped to a considerable degree. With examples where the mounting table was reinforced by a damping material bracket, and where the spring coefficient of the connecting pipe between the two units in the sample was changed, the resonance frequencies and transmissibilities were obtained by calculation using the analytical model, demonstrating the model’s general versatility as a prediction method.