Fuel efficiency becomes very important for new vehicles. Therefore, improving the aerodynamics of tires has started to receive increasing interest. While the experimental approaches are time-consuming and costly, numerical methods have been employed to investigate the air flow around tires. Rotating boundary and contact patch are important challenges in the modeling of tire aerodynamics. Therefore, majority of the current modeling approaches are simplified by neglecting the tire deformation and contact patch. In this study, a baseline computational fluid dynamics (CFD) model is created for a tire with contact patch. To generate mesh efficiently, a hybrid mesh, which combines hex elements and polyhedral elements, is used. Then, three modeling approaches (rotating wall, multiple reference frame, and sliding mesh) are compared for the modeling of tire rotation. Additionally, three different tire designs are investigated, including smooth tire, grooved tire, and grooved tire with open rim. The predicted results of the baseline model agree well with the measured data. Additionally, the hybrid mesh shows to be efficient and to generate accurate results. The CFD model tends to overpredict the drag of a rotating tire with contact patch. Sliding mesh approach generated more accurate predictions than the rotating wall and multiple reference frame approaches. For different tire designs, tire with open rim has the highest drag. It is believed that the methodology presented in this study will help in designing new tires with high aerodynamic performance.