Steady-state waves impinging obliquely on a coast are used to model a tsunami wave train as it moves from the open sea onto a continental shelf. The shelf edge is modelled with a discontinuity in depth, and on the landward side of the shelf edge the mean depth decreases linearly with distance to a value of zero at the coast line. Reflected waves in the open sea are found to have a reflection coefficient of unity as a result of a requirement that the solution be bounded at the shore line. The angle of wave incidence is found to have a significant effect upon wave amplifications near resonance frequencies but to have very little effect upon the magnitude of these resonance frequencies. Wave periods and wave length components parallel to the shore line are not changed as waves pass over the shelf, but wave length components normal to the shore line change significantly in this region.