An ambiguous representation of design geometry and its allowed variation is essential to design and manufacturing analysis tools using geometric modeling. In this paper, a new approach for modeling and representing mechanical tolerances, using information embedded in the solid model, is introduced. The work focuses on mathematical mapping between the nominal and variant configurations of design geometry, using boundary face-based model variables. The method identifies the relation between the errors of part geometry, represented by a solid model and measured using a coordinate measuring machine, and the tolerances, specified by dimensioning and tolerancing standards. The work is of benefit in understanding of the fundamental nature of geometric errors and tolerances; it guides the specification of dimensional and geometric tolerances; and, contributes to automated mechanical tolerancing in a solid modeling based system.