This paper presents our research approach and challenges in designing natural language interaction for a mechanical computer-aided design (CAD) system. We intend to use natural language input, ideally speech, as one method for capturing design problem definition from designers. Based on the problem definition, a new type of CAD system could explore a set of geometries that solves the problem. Our approach involves solving a natural language understanding problem: translating problem definition statements into a formal language that can be used for our exploration procedures.