Tolerance analysis of assemblies promotes concurrent engineering by bringing engineering requirements and manufacturing capabilities together in a common model. By further integrating the engineering modeling and analysis with a CAD system, a practical tool for product and process development is created. A comprehensive method based on vector assembly models has been development for modeling and analyzing variations in 2-D and 3-D mechanical assemblies. The models are constructed of common engineering elements: vector chains, kinematic joints, assembly datum’s, dimensional and geometric feature tolerances, and assembly tolerance limits. The method is consistent with engineering design practice and is well suited for integration with commercial CAD systems.. Systematic modeling procedures and rules for creating vector assembly models are outlined. Vector assembly models are created graphically and analyzed for variation statistically in an interactive design environment. Examples of a 2-D and a 3-D assembly are presented with corresponding vector assembly models.