This thesis describes the development of a computer program to optimise the design of a rocket powered orbiter vehicle, by combining a design synthesis with consideration of both the ascent and re-entry trajectories. This work is a extension of an existing trajectory optimisation program. Firstly the background to the problem is examined and a summary of previous work is presented. The objectives of this research program are examined and there follows a discussion of the mission requirements for such a vehicle and a description of the baseline design. The development of this problem as a integrated optimal control problem is discussed and is followed by a description of the mathematical models which are used to evaluate the vehicle. These include the geometry and packing model, the estimation of the orbiter's mass properties, the evaluation of the aerodynamics and the simulation of the trajectories. The mathematical details of these models are presented in detail i the appendices. The architecture and philosophy behind the writing of the program are then discussed. A user's guide is also presented as an appendix. Results are given for the solutions to a variety of orbiter design problems. These problems include a variety of separation conditions for air-launched vehicles, various re-entry cross-range conditions and a number of differing objective functions. A investigation into the optimality of the solutions and their sensitivity to changes in the optimisable parameters is also considered. The difficulty in obtaining optimal solutions is discussed in full.