This thesis is concerned with the use of Artificial Intelligence techniques to support human designers. The thesis argues that support for human designers can be improved by adopting an AI-based rather than a geometry-based approach to engineering design. Design Support Systems (DSSs) are proposed as an effective means of delivering this improved support. Representing and reasoning about tolerance statements in design is introduced as a valid area to test these claims. Tolerance statements describe the allowable variations in the geometry of a designed artefact. Two distinct, but related problems involving the use of tolerance statements in design are tackled, namely: tolerance combination (including the way tolerance distributions combine), and tolerance allocation. The problem of tolerance combination (and distribution) involves determining the necessary consequences of the application of known tolerance statements to one or more designed artefact features. Tolerance allocation concerns the assignment of tolerance statements during the design process. Solutions to this second problem are essential before manufactured instances of designed artefacts can be tested for compliance with design descriptions. The use of an experimental DSS, the Edinburgh Designer System (EDS), to solve design problems is illustrated. The implementation of techniques to improve the support of tolerance combination and tolerance allocation is described and where possible has been tested using EDS. The way that design is situated within the product creation process is investigated and the derivation of parts list information from an EDS design description is demonstrated. The thesis concludes that the AI-based approach can improve support for human designers, but that further research will be required to demonstrate the effective delivery of this support through DSSs.