Erosion, deposition, and tectonic processes interact to define the style of deformation in compressional belts. This paper introduces a method of integrating a numerical model for surface transport with analogue sandbox models of compressional belts to further improve our understanding of this interplay. The analogue model provides the numerical model with the rising topography, whereas the numerical model calculates the river network and the resulting amount of erosion and sediment transport. Compared to previous analogue models with uniform (two-dimensional) erosion this method provides a tool to incorporate process-based rates of erosion and deposition with spatial distributions that depend on the river network developed on the evolving topography. Rivers running parallel to the evolving mountain belt induce along-strike changes in erosion and deposition that in turn result in asymmetric tectonic deformation. The additional load of sediments controls the propagation of thrust as well as the direction of vergence of the main thrust. High erosion rates do not always lead to fewer thrusts within the compressional belts but generally steepen and lengthen the lifetime of the affected faults.