This paper presents geometric models for representing machining operations. The characteristic shapes produced by machining operations are represented in a uniform (canonical) way for all machining operations as the resultant to two types of tool-workpiece interactions. Each interaction is characterized by a type of sweep operator. The directors of these sweep operations are derived from cutting and feed motion directions. The profiles used in the sweeps are defined in terms of geometric entities and constraints based on tool geometry and tool-workpiece interaction. Most conventional machining processes can be represented using the proposed model (process-to-volume mapping). Inverse operators are also defined for mapping volumes to processes; the inverse operators can be used in selecting potential machining processes for removing given volumes. Thus, representation of machining knowledge is process-based not feature-based, which overcomes the problem of dealing with new feature shapes that are not predefined in the process selector.