The purpose of this investigation was to develop an undercarriage design technique to minimise aircraft response while taxying without causing deterioration of the landing response. Following a brief review of the available literature a detailed analysis is made of a general, three-dimensional, multi-degree-of-freedom, mathematical model which allows fully for friction, stiction and non-linear damping in various components of the undercarriage. Provision is also made for undercarriage bogie action, aerodynamic forces on the aircraft and tyre forces. An optimisation procedure is proposed with maximum stress and fatigue of the aircraft structure and passenger or pilot ride as constraint parameters. Results are presented for typical aircraft to show the applicability of the mathematical model and suggestions made for simplifications in it, in order to reduce computation time. Suggestions are also made for future work.