Considering the present-day environmental and energy objectives set forth by governments and aiming at minimizing carbon footprints and fuel consumption in the transportation sector, it is of utmost importance for manufacturers to enhance tire design. This is because doing so has the potential to revolutionize the automotive industry by promoting advancements in structural performance and fuel efficiency while reducing environmental impact and ensuring safer, more dependable vehicle structural performance. Moreover, such an approach has the advantage that the choice of model’s features such as the geometry and material mechanical properties, is done in a more detailed manner. The mechanical behavior of rubber compounds used in tire manufacturing has a direct impact on the static as well as the dynamic response of tires in various operating scenarios, such as steady state and transient dynamic. However, in the literature, there is a plethora of works that often consider basic rubber constitutive laws without a consistent study of the impact on the model results. Therefore, this paper proposes a comparative study of the static response of a radial tire using finite element method for different choices of incompressible rubber material behavior ranging from elastic(EL), hyperelastic(HE), visco-hyperelastic(VH) to hyper-pseudoelastic(HM). Simulations of an inflated tire and vertically loaded were conducted in ABAQUS Explicit, and the resulting radial deformation, maximum Von Mixes stress, CPU time, contact patch, and contact pressure were selected as four consistent comparisons. The results show that among the four material cases, the VH and HM material models lead to the most accurate result with a shorter CPU time with the latter. Also, their contact pressure and body stress are higher than those of the elastic and hyperelastic models, and this brings an important solution to the disparity between the calculated and experimentally measured contact pressure in previous works.