Planetary exploration rovers are the most efficient means of off-world surface exploration. As mobile laboratories, they are used to perform various experiments and gather data semi-autonomously from remote extraterrestrial environments, both for planetary science and assessing conditions in preparation for human exploration. To accomplish the mission and access sites of scientific interest, the rover must be able to traverse various types of unstructured terrain without becoming embedded or succumbing to other hazards. Modelling of the rover is essential to understand how the rover interacts with its environment and how to select the best path. 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 travelled being approximately 0.4 %. The results of the combined dynamic and terramechanics model, incorporating slip, are limited to the conceptual development of the model due to time constraints, and are thus inconclusive at this time.iii