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Detailed results of numerical calculations of transient, 2D incompressible flow around and in the wake of a square prism at Re = 100, 200 and 500 are presented. An implicit finitedifference operator-splitting method, a version of the known SIMPLEC-like method on a staggered grid, is described. Appropriate theoretical results are presented. The method has second-order accuracy in space, conserving mass, momentum and kinetic energy. A new modification of the multigrid method is employed to solve the elliptic pressure problem. Calculations are performed on a sequence of spatial grids with up to 401 Â 321 grid points, at sequentially halved time steps to ensure grid-independent results. Three types of flow are shown to exist at Re = 500: a steady-state unstable flow and two which are transient, fully periodic and asymmetric about the centre line but mirror symmetric to each other. Discrete frequency spectra of drag and lift coefficients are presented.