The central issue discussed in this paper is how a designer may profit from the use of mathematical simulation and optimization techniques. These techniques can be useful tools to support the designer in solving his design problem. The place and the potential of these techniques in the design process, as well as their use by the designer, are discussed. The principles underlying these techniques are outlined and an overall view is given of the various methods that can be applied. Examples of applications are presented to illustrate their usefulness in design processes and attention is paid to the integration of these design methods into structured systems for computer aided design. Paper presented at the second International Conference on Computer Applications in Production and Engineering (CAPE '86), Copenhagen, May 20-23, 1986.