With the recent advances in rapid modeling and rapid prototyping, accurate simulation models for tires are very desirable. Selection of a tire slip model depends on the required frequency range and nonlinearity associated with dynamics of vehicle. This paper presents a brief overview of three major slip concepts including ‘Stationary slip’, ‘Physical transient slip’ and ‘Pragmatic transient slip’; tire models use these slip concepts to incorporate tire slip behavior. The review illustrates that there can be no single accurate slip model which could be ideally used for all modes of vehicle dynamics simulations. Currently, a semi-analytical tire model (KU-Tire) for intermediate frequency (up to 100Hz) is under development at Kettering University. Firstly the scope of this project is to investigate different steady state and transient slip models developed and used in industry and academia, to find the most appropriate model, which could be added to this basic rigid ring tire model for capturing the tire behavior on uneven roads with relatively short and sharp unevenness. After a comprehensive investigation of all these existing tire models, we present the pragmatic transient tire modeling approach, which is best suited for performing vehicle ride simulation up to frequency range of 100 Hz. Then, the most appropriate relaxation length based pragmatic slip model is developed to capture the transient longitudinal slip behavior. Finally, pragmatic slip model is integrated to the rigid ring model and its response is analyzed against the road profiles with step obstacles of various shapes (triangular bump, large plank, small trapezium and large trapezium). This study concludes that the tandem cam enveloping model with pragmatic slip model makes very accurate approximation of contact behavior of tire and this contact model coupled to rigid ring model make a good combination of complexity and simplicity, as they incorporate both physical and empirical approaches.