In this study, a two-dimensional numerical computation was carried out for steady and unsteady laminar flow around a square obstacle with infinite domains. The non-linear equations defining the flow field were solved iteratively by using the finite-difference technique. The velocity-pressure relationship was expressed via the vorticity-stream function relationship and special attention was paid to the boundary conditions for the vorticity. The computations were carried out for several values of the Reynolds number. The behaviour of the vortex flow formed downstream of the square obstacle was predicted. The results were then compared with experimental data and the flow field visualized. The agreement between the numerical an other results are reasonable.