Physically-based soil erosion models are valuable tools for the understanding and efficient management of soil erosion related problems at the basin and river reach scales, as soil loss, muddy floods, freshwater pollution or reservoir siltation, among others. We present the implementation of a new fully distributed multiclass soil erosion module. The model is based on a 2D finite volume solver (Iber+) for the 2D shallow water equations that computes the overland flow water depths and velocities. From these, the model evaluates the transport of sediment particles due to bed load and suspended load, including rainfall-driven and runoff-driven erosion processes, and using well-established physically-based formulations. The evolution of the mass of sediment particles in the soil layer is computed from a mass conservation equation for each sediment class. The solver is implemented using High Performance Computing techniques that take advantage of the computational capabilities of standard Graphical Processing Units, achieving speed-ups of two orders of magnitude relative to a sequential implementation on the CPU. We show the application and validation of the model at different spatial scales, ranging from laboratory experiments to meso-scale catchments.