An analysis is made of the compression wave generated when a high speed train enters a tunnel. Operations in the near future are expected to be at Mach numbers M ranging in value up to 0โข4. Non-linear steepening of the wave in a very long tunnel exacerbates the environmental damage caused by the subsequent radiation of an inpulsive micro-pressure wave from the far end of the tunnel. The compression wave profile depends on train speed and the area ratio of the train and tunnel, and for M Q 0โข2 can be estimated to a good approximation by regarding the local flow near the tunnel mouth during train entry as incompressible. The influence of higher train Mach numbers is investigated for the special case in which the tunnel is modelled by a thin-walled circular cylinder, of the type frequently used in model scale tests. This is done by representing the nose of the train by a distribution of monopole sources, and calculating their interaction with the mouth of the tunnel by using the exact acoustic Green's function for a semi-infinite, circular cylindrical tunnel. Empirical formulae valid up to M = 0โข6 are obtained for the compression wave amplitude and for the maximum initial pressure gradient (which determines the amplitude of the micro-pressure wave). Predictions of the theory are found to be within 5% of measurements made in recent experiments.