The processes of erosion and deposition must be included in foreland basin models to predict correctly basin geometry and stratigraphy. We present a synthetic stratigraphic model of the development of nonmarine foreland basins that predicts progressive geometry, topography, and facies patterns. In the model, steady crustal shortening occurs according to a wedge-thickening model, erosion and deposition follow a diffusive process, and the lithosphere is compensated elastically. Erosion and deposition are controlled by the transport coefficients κ of the diffusion equation. For a range of thrust velocities and lithospheric rigidities, transport coefficients are of order 102–103 m2/yr in the mountain belt; these values are much higher than those derived from the study of scarp degradation. In the sedimentary basin, transport coefficients of order 104 m2/yr are appropriate and are compatible with previous studies of fluvial and deltaic deposition. Rapid thrusting results in a narrow underfilled basin, while slow thrusting results in a wide overfilled basin. In addition, by varying the erosional and depositional transport coefficients while holding other parameters constant, we generate both overfilled and underfilled basins. These results suggest that changes in the rate of thrust loading, the climate, or the source rock lithology can create stratigraphic signatures that have been interpreted to record viscoelastic relaxation of the lithosphere. Clearly, to understand either the long-term behavior of the lithosphere or to interpret orogenic history from preserved foreland strata, the manner in which a basin was filled must be considered. We apply the model to the evolution of the modern sub-Andean foreland and find that an erosional transport coefficient of 3000 m2/yr and a depositional transport coefficient of 20,000 m2/yr successfully predict the observed basin geometry.