The aim of this paper is to numerically explore the non-linear two-dimensional unsteady potential flow over a Savonius rotor and to develop a code for predicting its aerodynamics performances. In the model developed, the rotor is represented in a median plane by two semicircles, displaced along their common diameter. The two semicircles can be considered to produce lifting effects. As a result, they are modelled by a collection of discrete vortices on their contours. The flow field is then governed by the Laplace equation. The versatile Neumann boundary condition, applied over the contour of the semicircles and the Kutta Joukowsky condition applied at the four extremities of the semicircles have been used in the modelling. The torque distribution of the stationary rotor and the unsteady pressure field on the blades of the rotating rotor, predicted by the code developed, have been compared and validated by some experimental data. (C) 2009 Published by Elsevier Ltd.