A new model is developed for the resonant response of ground motion in enclosed sedimentary basins. In their study of deeply embanked sediment-filled valleys, Bard and Bouchon (1980 a, b; 1985) show that reflections and refractions at the valley's edges generate important conversion of incident SV waves to horizontally propagating P waves which establish lateral resonance patterns. Our model is related to these results through the use of two approximations: reflecting edges and horizontal P waves. This model allows us to calculate lateral resonances in a given sedimentary basin for any shape of its borders. We apply this model to the actual shape of San Fernando Valley and account for the large differential amplifications reported by Kagami et al. (1986) in their two-dimensional study of microtremors in this basin. We obtain a map of amplifications in the surface of the San Fernando Valley that shows a remarkable coincidence with the microtremor experimental data.