In designing a muffler, the acoustic engineer must consider two objectives: (1) the specified insertion loss and (2) the estimates of change in engine performance brought about by an exhaust muffler on the performance of a small two-cycle gasoline engine by predicting the exhaust muffler pressure oscillations in a muffler. Such engines are commonly used for garden tools, power boats, and motocycles. The exhaust muffler consists basically of two elements: an expansion chamber or cavity and a tailpipe open to the atmosphere. A mathematical model is presented which includes the simulation of two-cycle-engine and exhaust muffler pressure oscillations. Two methods are given for coupling the nonlinear mass flow through the exhaust ports with an acoustic wave equation model employed for the exhaust pressure simulation. With the first method, the Helmholtz resonator approximation is used to model the wave equation in the exhaust system and is solved simultaneously with the engine thermodynamic equations using the Runge-Kutta method. With the second method, a steady-state solution for the acoustic impedance at the exhaust ports is coupled with the nonlinear flow through the exhaust ports to obtain a solution. The calculation of the pressure oscillations in a muffler will help in estimating the change in engine performance brought by the muffler. Comparisons between theory and experiment are given.