Acoustic simulation methods are being increasingly used for practical exhaust system design of automotive. In many practical applications, the sound source emits, partly, a low frequency sound spectrum comprised of superposed discrete tones and partly, a higher frequency broadband spectrum. The turbulent vortices that develop in the boundary layer between the duct wall and the flowing medium are said to generate a selfexcited noise, that noise is broadband character. The self-excitation is enhanced when the flow is disturbed by irregularities in the duct wall. Unsteady compressible fluid flow through a duct is often encountered in many engineering applications and has been investigated by many researchers. When a pressure wave generated inside a duct is discharged from an open end of the duct, an impulsive wave that is usually characterized by high sound pressure level of short duration forms at the vicinity of the exit of the duct. Acoustic simulations solve the equations for motion, mass, momentum, and energy and can be divided into two methods, linear and non-linear. Through that literature review, we can analyse the methods and the latest development done on exhaust systems with regard to acoustic performance. The basic theory behind both approaches is explained as well as a source characterization technique that can be used to link the two methods. Some acoustic software tool has been applied to a variety of exhaust systems.