The STI (System Technology Inc.) tire model is one of the most important semi-empirical (steady-state) tire models currently applied in the vehicle dynamics simulation software package of the National Advanced Driving Simulator (NADS). The STI tire model is presented originally based on tire contact length directly and the contact length is required to provide. Based on the concepts of nominal slip in both longitudinal and lateral directions, the STI tire model is analyzed and rewritten. It shows that the STI tire model does not actually depend on the contact length. Meanwhile, the model parameters are partially assigned new physical definitions, for example, static/dynamic stiffness and shape factors. Some simplified expressions are given based on further assumption conditions. The simplified expressions are also obtained regarding longitudinal slip at arbitrary speeds (including low speed, zero speed and stand still), which is originally presented by Bernard.