The problem of exhaust flow from a high speed two-cycle engine is investigated for a specific exhaust pipe geometry. The attempt is to simulate accurately the ramming and scavenging effects of the pressure waves at the exhaust port in the cylinder of such an engine, over a range of engine speeds. Using a one-dimensional, compressible, inviscid fluid model, the GODEL hydrodynamic computer code developed by Chapman is employed to accomplish the simulation. Two differencing schemes are examined and compared. Further, we discuss briefly the implications of our results as regards (i) the applicability of certain solution algorithms to the particular problem; and (ii) the future of employing such numerical techniques to the analysis of exhaust and other internal combustion engine flows.