Steady two-dimensional flow in driven cavities is often handled numerically with the laminar model even at relatively high Reynolds numbers. The onset of turbulent flow still surrounded by some ambiguities concerning the appearance of the first Hopf bifurcation. Under the light of these facts, the present paper mainly aims to numerically illustrate the difference effectiveness of the Spalart-Allmaras (SA), the Renormalization Group K-epsilon (RNG K- ), the Shear Stress Transport K-omega (SST K- ), and the Reynolds stress (RSM) turbulence models (RANS turbulence models) against the laminar model. The problem under examination is represented by a two-dimensional flow in two-sided lid-driven square cavity. The top and bottom walls slide in opposite direction (antiparallel wall motion) with different velocities related to two various velocity ratios =-7 and -10. The predicted numerical results are computed with the Finite Volume method (FVM) based on the second scheme of accuracy. From the examination of the computational results, it is seen that the SST K- model, the Stress-omega Reynolds stress model (Omega RSM), and the laminar model shows a high efficiency compared to the salient weakened for the Spalart-Allmaras (SA) model, the RNG K- model, and the Linear pressure strain Reynolds stress model (LPS-RSM) near end walls. However, the laminar model outperforms all of RANS turbulence models when =-10. As a result, we believe that the laminar model is numerically the most convenient model for two-dimensional driven cavities problems at relatively high Reynolds numbers until a solution ceases to converge.