The scattering of topographic Rossby waves over a shelf that abruptly changes its width with a step-shaped coast is studied by two methods: mode expansion (which in principle is exact) and ray theory. For the latter, we stress the importance of evaluating the phase field instead of limiting the results to the ray paths, as is often done. Ray theory is found to give a good approximation of the energy flux at low frequency and the correct location and strength of highs and lows of the transport function. However, ray theory predicts very sharp gradients of this field (which imply unrealistically high velocities) at the frontier of the region illuminated by a beam. These results suggest that ray theory may be an alternative, or complement, to numerical models for those scattering problems where a complicated topography and/or coastline prevents the use of the mode expansion method. ¿ American Geophysical Union 1993