Inertia-gravity waves trapped by a constant depth gradient against a vertical barrier are studied in an asymptotic limit (high frequency, weak depth gradient) of the shallow water equations; an f-plane is assumed. Both a numerical solution and an approximate analytical solution, which are in broad agreement, are presented. The waves display properties different from channel Kelvin and Poincaré waves and different from coastal waves. Implications of inertia-gravity wave trapping for geostrophic adjustment in a channel fluid model are explored.