A numerical method is presented for the prediction of exhaust noise in internal combustion engine exhaust systems. The prediction is based on a linear model for the exhaust system which is dependent on a nonlinear model for the engine. A fired engine is modeled by a combustion process, and the energy balance in the gas content of each cylinder. A set of nonlinear differential equations are obtained to model the engine, and a set of linear differential equations are obtained to model the exhaust system. The mathematical model for the engine is coupled with the exhaust system by appropriate boundary and initial conditions at area discontinuities. The governing equations for the system are solved by an explicit solution procedure for in-cylinder thermodynamical processes, and acoustical field quantities in the exhaust system.