Abstract In this paper acoustic shock waves are considered in a variable area duct which contains near sonic flows. The problem treated here is modelled after an aero engine inlet. It is known experimentally that area variation of a duct and high Mach number mean flow can reduce acoustical energy yielding substantial noise reduction. One possible reason for this is acoustic shocks. The use of an explicit numerical method is described which is very accurate and also captures shocks reasonably well. Comparisons of the results are made with an existing asymptotic theory for Mach numbers close to unity. When shock occurs reduction of sound pressure levels are shown by examples.