In this paper the agreement between laboratory experiments performed with three-dimensional granular avalanches moving along a partly curved surface and their numerical predictions shall be examined. First, the most important elements of the theory describing the flow of a cohesionless granular material down a rough bed are presented. Based on the depth-averaged model equations, an advanced numerical integration scheme is developped by making use of a Lagrangian representation (i. e., the grid moves with the deforming pile) and a finite difference approximation that handles the numerically two-dimensional problem accurately. Second, experiments are described that were conducted with a finite mass of granular material moving down, respectively, an inclined plane and a surface consisting of an inclined and a horizontal plane connected by a curved transition area; the initial geometry of the avalanche is generated by a spherical cap. Third, for a number of different experiments a comparison is carried out between the experimentally determined positions of the granular avalanche during its motion and the numerical prediction of these positions. It shows that the numerical results fit the experimental data surprisingly well.