Classical experimental design methods have gained widespread acceptance in the simulation literature. The simulation experimental design literature concentrates almost exclusively on factorial, fractional factorial, and composite simplex designs, which can be significantly more efficient than random or ad-hoc methods. However, there are several substantial differences between the classical (statistical) and simulation contexts that have received little attention. Most importantly, the design literature concentrates on obtaining maximum information from a set number of experiments, while in simulation we often wish to obtain a given amount of information at minimum cost. Also, classical designs and design methods generally assume constant variance and constant cost-per-experiment, while this is generally not the case in simulation. Hence classical designs are often not suitable for the simulation context. In addition, there are few rules to guide the experimenter in choosing an appropriate design, leading to quite arbitrary selection procedures. Thus although computer simulation is the ideal environment for which to develop experimental design software, the limitations of classical design methods mean that such software would do little more than perform routine tasks. In this thesis we discuss the main differences between the classical and simulation contexts, and propose and develop an alternative design approach that is often more suitable for the simulation context. The design for our approach is found by solving an optimisation problem, and includes an element of sequentiality. In conjunction with a proposed solution heuristic, our approach is easily incorporated into experimental design software that requires little input from the experimenter. A number of examples and a Monte Carlo study are presented to illustrate the properties of our approach. We also discuss sequential experimental design, and list a number of research issues.