The behaviour of a rapidly rotating homogeneous flow past a cape is investigated by means of a numerical model based on the quasigeostrophic formulation. The cape geometry is introduced by rewriting the vorticity equations in a curvilinear coordinate system. The model is then solved by a classical finite-difference method. The evidence for a regime transition between a steady flow situation and an eddy-shedding unstable situation is pointed out. The transition Reynolds number is about 400 (based on the cape dimension) which is similar to what was observed in several related experimental investigations. The eddying regimes may be characterised by their Strouhal frequencies which are also found to be close to the experimental values.