A computational technique was developed for the method of characteristics solution of a one-dimensional compressible, unsteady flow in a duct as applied to the wave action in an engine exhaust system. By using the method it was possible to compute the detailed flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operating engine has been achieved in the calculation of both the third-octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of non-linear behavior which results in wave steepening and shock wave formation. The calculation method developed differs from those of others, principally that of Blair and that of Karnopp, Dwyer and Margolis. Its essential feature is the computation of the precise paths on the x−t plane of a finite number of C+, C− and P characteristics, to provide high accuracy in determining the tailpipe outlet velocity and hence radiated noise.