We study the effects of incorporating surface mass transport and the gravitational potential energy of both crust and lithospheric mantle to the viscous thin sheet approach. Recent 2D (cross-section) numerical models show that surface erosion and sediment transport can play a major role in shaping the large-scale deformation of the crust. In order to study these effects in 3D (planform view), we develop a numerical model in which both the dynamics of lithospheric deformation and surface processes are fully coupled. Deformation is calculated as a thin viscous layer with a vertically-averaged rheology and subjected to plane stresses. The coupled system of equations for momentum and energy conservation is solved numerically. This model accounts for the isostatic and potential-energy effects due to crustal and lithospheric thickness variations. The results show that the variations of gravitational potential energy due to the lateral changes of the lithosphere–asthenosphere boundary can modify the mode of deformation of the lithosphere. Surface processes, incorporated to the model via a diffusive transport equation, rather than just passively reacting to changes in topography, play an active role in controlling the lateral variations of the effective viscosity and hence of the deformation of the lithosphere.