The application of the wind-driven cross-ventilation in modern buildings has been raised due to their potential in energy saving and improvement of the thermal comfort and air quality inside the buildings. Despite the relatively simple concept of the cross-ventilation mechanism, its underlying physics is very complex, resulting in necessity to the detailed numerical and experimental analysis. Computational fluid dynamics (CFD) simulations and simplified models based on the orifice mode have been extensively used by researches, but their accuracy is still a challenging issue. In this study, thus, the accuracy and applicability of the steady RANS and the orifice models were investigated for scenarios of unsheltered and sheltered buildings. The CFD models were validated against the experimental data from literature using validation metrics for the air flow parameters inside the building. Accuracy of different turbulence models were investigated in terms of velocity and turbulent kinetic energy (TKE) distributions, airflow rate, and wind surface pressure. Also, the accuracy of the orifice model in prediction of the airflow rate was examined. According to the results, the CFD simulations provided acceptable results for the velocity and turbulent kinetic energy distributions inside the building, but the accuracy of the models in estimating the airflow rate was relatively low when the windward opening was located close to the roof. In contrast to the unsheltered building condition, all turbulence models failed to simulate the velocity, turbulent kinetic energy and the crossing airflow rate for the sheltered condition. In this case, the validation metrics were found to be far from the acceptable thresholds. The relative error in calculating the airflow rate was found in the range of 76% to 107% for different turbulence models. According to the results, the application of the steady CFD simulation and the orifice model is limited for the sheltered building condition. Therefore, it can be concluded that more studies required to improve the accuracy of the steady RANS models and the uncertainty of the input parameters to the orifice model for the unsheltered and sheltered building conditions.