A theoretical model is developed for the infilling of a basin by the propagation of a delta. The model simulates four mechanisms for the transfer of sediment from the land to the sea: (1) bed load dumping along the delta front, (2) hemipelagic sedimentaton under the seaward flowing river plume, (3) proximal slope bypassing by turbidity currents, and (4) the combined effects of both short-term (wave and tidal action) and long-term (creep and small slides) downslope diffusion of the accreting sediment mass. The general model is of relatively low precision, useful for predicting basin infilling on time scales greater than a few hundred years. The river plume portion of the model can predict sedimentation on time scales of less than a year and is designed to reflect the dynamics of a free, two-dimensional, buoyant jet that transports a composite size population of suspended particles. The general model allows the prediction of lithologies changing with time and space. The model has been used to simulate infilling processes for Knight and Bute inlets, two grabenlike (fjord) basins along the coast of British Columbia. Model simulations of delta progradation over the last 10,000 years favorably predicted the modern seafloor bathymetry and sediment accumulation rates to within a factor of 2 of measured (210Pb, 137Cs, and sediment trap) rates. ¿ American Geophysical Union 1988