Computer simulation models are increasingly necessary as a design tool for modern vehicles, for which a subcategory relates to motorcycles. Simulation models can be employed for a variety of applications, an important area of which relates to the motorcycle's dynamic responses. The response of a motorcycle is heavily dependent on the rider's control actions, and consequently a means of replicating the rider's actions provides an important extension to this area. The application of mathematical control techniques for replicating the motorcycle rider's control actions is presented in this thesis, detailing specifically the techniques of optimal control and model predictive control. The work begins with modelling the dynamics of the motorcycle using standard procedures. The application of optimal control to a motorcycle rider is not new, but the available results have been extended significantly over those previously available, allowing further insights into the behaviour and therefore applicability of this strategy to modelling a motorcycle rider. Use of the model predictive control approach is new in the field of motorcycle rider modelling, and a similarly extensive parametric study is conducted to evaluate the suitability of this approach, and to highlight the similarities and differences between this and the optimal control approach. Both controller models were simulated over a standard single lane-change manoeuvre. Comparison of the relative performances of the two control approaches confirmed strong similarities between the techniques, particularly when the modelled rider is permitted an extensive knowledge of the approaching road path to follow. When this knowledge is restricted, differences were apparent between the two, suggesting the predictive control approach is capable of better performance here, and therefore represents a more robust control strategy. An option of the predictive control approach allows more elaborate target paths for the rider to follow to be set. However, defining the target path for the rider model to follow as the road centreline, and then permitting the controller itself to select the most appropriate course to take, has also been shown to be the more suitable option. The predictive control technique for motorcycle rider modelling is shown to be a theoretically suitable application. Further work is suggested to validate the results presented here. If it can be confirmed that the model accurately captures a motorcycle rider's actions, this will prove a very useful tool for the understanding of a motorcycle rider's control actions, with potential benefits towards rider safety and furthermore as a design tool for the motorcycle industry.