This thesis presents the development of three-dimensional kinematic and dynamic models, using MATLAB and SimMechanics, describing the Argo J5 four-wheel rover, in response to terrain elevation inputs and slip. The kinematic models describe the pose and velocity of the rover using the Denavit-Hartenberg convention, while the SimMechanics dynamic model is combined with a terramechanics model to develop accelerations and obtain the forces and torques, based on terrain properties. The kinematic analyses were performed for simulated traverses including cases of flat, inclined, side slope, and sinusoidal terrain, with varying amounts of slip in the velocity analysis. The results showed good agreement with expected trends and values for the joint displacements and rates, with the largest percent deviation for the distance traveled being approximately 0.4 %. The combined dynamic and terramechanic model, is limited to the conceptual development of the model due to time constraints, and results are inconclusive at this time.