A numerical model describing two-dimensional, shallow water, long wave propagation has provided estimates of the co-oscillating palaeotides in the upper Devonian Catskill Sea. This sea was open to the ocean along the present Gulf Coast and, moving clockwise, was circumscribed by the Transcontinental Arch, the Old Red Sandstone Continent, and the rising Appalachian Orogen. Using the present best estimates of basin bathymetry and open-ocean tidal range, the model indicates high mesotidal to low macrotidal ranges for the Catskill Shelf along the ancestral Appalachians. The Mid-Continent Shelf, centred on Iowa, is considered to have been microtidal. These conclusions are not sensitive to reasonable variations in shelf geometry and support the hypothesis that at least some epicontinental seas could have been tide-dominated.