An offshore wave energy spectrum is tracked inshore taking account of shoaling and refraction due to bathymetry and currents, energy losses due to whitecapping and bottom friction, wind-wave generation, quadruplet wave-wave interactions; and the nearshore processes of depth-induced breaking and triad wave-wave interactions. The finite-element code TOMAWAC is used which is efficient and well suited for largescale modelling. Diffraction is not modelled and may be significant over shallow sandbanks of interest here. Comparisons are made with wave fields measured experimentally over elliptical and circular shoals. Predictions by TOMAWAC are quite accurate for directional waves with broad spreading, but less so with narrow spreading. A diffraction code including otherwise similar physics, ARTEMIS,performs better for narrow spread waves, although not necessarily for broad spread waves. Field tests for TOMAWAC are also encouraging. Given that TOMAWAC with broad spread waves appears to avoid, or at least considerably reduce, the need for diffraction, the nearshore wave fields due to broad and narrow spread waves offshore were compared for the East Anglian coastal region. Close to the shore, wave heights were almost identical, suggesting that an efficient ray tracking code like TOMAWAC with broad spread waves is a valid tool for nearshore wave field prediction.