The reflection and transmission of ocean waves at a sea ice boundary is reconsidered. The sea ice is modelled as a continuous, thin elastic plate of uniform thickness, floating on water of arbitrary constant depth. Unlike earlier solutions, matching of potentials between the free surface domain and the ice-covered domain is done at all detphs; previous solutions were incompletely matched, as the potentials in each domain were deficient. In the present solution a number of the infinity of evanescent modes, which were hitherto ignored, are included in the solution and allow matching to be carried out by minimization of an integrated error term from surface to seafloor. Reflection and transmission are found to be markedly influenced by the inclusion of these modes, suggesting that conclusions based on the incomplete potentials may be substantially in error. ¿American Geophysical Union 1990