This paper presents the development of a tire model for use in the simulation of vehicle dynamics. The model was developed to predict tire lateral and longitudinal force responses to dynamic inputs. In this new tire model, the contact patch of a tire is lumped into a number of elements to study the dynamic behavior of the displacement of the tire contact patch in the lateral and longitudinal directions. For each displacement, a differential equation governing the dynamic behavior of the displacement to the dynamic inputs is derived. Based on the differential equations for the lateral and longitudinal displacements, difference equations are derived for the purpose of simulating tire output responses. Since system parameters, such as mass, damping and stiffness, in the difference equations are unknown, estimation of system parameters is performed using the differential equations and experimental data measured for this research. This tire model is validated by comparing the simulated tire output responses with available experimental data in both quasi-static and dynamic maneuvers.