The design and construction of fixtures is a major hindrance to the reconfigurability of flexible manufacturing systems. A promising method is to use a modular fixturing system. There remains, however, a considerable problem in the design of appropriate assemblies of such fixturing elements. This project describes a program for the automatic design of assemblies of modular fixturing elements. Its input is a description of the workpiece geometry, the machining envelope and the fixturing points. Its output is an automatically generated fixture design. The program incorporates systematic design procedure in conjunction with a large library of rules governing the movement and combination of the modular elements. A key feature of the system is the development of a suitable spatial representation technique, to describe those regions of space which are occupied by the workpiece itself, by the fixture and by the tools used to produce it. This spatial representation system permits the program to search and identify objects and object intersections. It is also able to determine the relative position of the modular elements during the design process. A design example was given to illustrate the method.