The results of unsteady Reynolds averaged Navier-Stokes (URANS) simulations of flow around a square cylinder using two-dimensional hybrid meshes were presented in this paper. The first part examined the accuracy of various RANS turbulence models, i.e. the standard model, RNG model, realizable model, standard model, SST model, and RSM, by comparing their results with available experimental data. Despite the limits imposed by the RANS approach and the relatively inexpensive two-dimensional computations, the main features of this complex flow can be predicted reasonably well. Among the computations using various RANS models compared here, the SST model shows the best agreement with the experiment. The second part investigated the effects of corner cutoffs on unsteady flow characteristics around a square cylinder by using the SST model. Especially the detailed near-surface flow structure around the cylinder was focused on, aiming at giving an explanation for the drastic modification of the aerodynamic characteristics as the corner shape is slightly changed.