This paper discusses the abilities of two different low-Reynolds-number eddy-viscosity models in resolving the complex physical features that arises in turbulent flows around a square cylinder at Re=22000. For the modeling of turbulence, the Launder & Sharma (LS) [1] and Kawamura & Kawashima (KK) [2] low-Re models have been employed. The present numerical results were obtained using a two-dimensional finite-volume code. The pressure field is obtained with the well-known SIMPLE algorithm. Advective volume-face fluxes are approximated using a bounded version of the upstream quadratic interpolation scheme, QUICK. Comparisons of the numerical results with the experimental data indicate that the steady computations, as expected, cannot produce reliable flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are approximated using the second-order Crank-Nicholson scheme. The unsteady computations significantly improve the predictions and the results of unsteady simulations with both turbulence models are in closer agreement with measurements compare to the steady predictions. The predicted value for St number is 0.126 and 0.123 using the LS and KK turbulence models respectively which are in good agreement with the measured value of 0.132. The unsteady predictions using the LS model are in better agreement with the measured data than those obtained with the KK model. Both turbulence models fail to produce reliable turbulence field predictions and, thus, it is necessary to apply more advance turbulence models, such differential stress models, for more accurate predictions of such flows.