The recent literature has introduced models based on nonlocal conservation laws in several space dimensions, e.g., see [3] for crowd dynamics applications or [1] for sedimentation processes. The Lax-Friedrichs type numerical algorithm presented in this talk is proved to be converging to the exact solution. The usual divergence free assumption, see [2], is here abandoned. The key step in the convergence proof is providing strong BV estimates on the approximate solutions. Numerical integrations show the convergence rate as well as various qualitative properties of the class of equations considered. References [1] F. Betancourt, R. Burger, K.H. Karlsen, E.M. Tory, On nonlocal conservation laws modelling sedimentation, Nonlinearity 24, 3, 855--885, 2011. [2] C. Chainais-Hillairet, Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate, Mathematical Modeling and Numerical Analysis, 33, 1, 129--156, 1999. [3] R.M. Colombo, M. Garavello, M. Lecureux-Mercier A Class of Non-Local Models for Pedestrian Traffic, Mathematical Models and Methods in the Applied Sciences, 22, 4, 2012.