This work presents computer simulations of four batch sedimentation processes in inclined rectangular vessels. The simulated cases covered dilute, dense, viscous and inert sedimentation of monodisperse suspensions. Details of the stratified flow within the vessel, such as clear fluid layer thickness and velocity profiles, are evaluated against available theoretical results and against measurements carried out in our laboratory. The simulations were based on a complete mechanistic two-fluid model which we implemented in a commercial CFD code. We also measured the clear fluid layer and the sediment layer thickness for a dilute particle-water suspension using a photographic technique. The overall features of the computed sedimentation process compared well with our experimental observations, and the computed clear fluid layer thickness was in good agreement with theoretical and experimental results. However, the velocity profiles and the motion of the top interface were slightly underpredicted. The results for the sediment layer confirm the trends of the theoretical results. We also clearly observed particle slip at the upward-facing vessel wall.