This paper presents a scheme for establishing geometrictolerance zones for polyhedral objects in solid modelers. Theproposed scheme is based on a surface-based variational model.Variations are applied to a part model by varying each surface'smodel variables. Those model variables are constrained bysome algebraic relations derived from the specified geometrictolerances. For size tolerance, two types of tolerance zones areconsidered in order to reflect two different types of sizetolerances. For any other geometric tolerance (form, orientationor positional), the resultant tolerance zone is defined by thecombination of size tolerance and that particular geometrictolerance specifications. Appropriate algebraic constraints (onthe model variables) are finally used to establish the tolerancezone boundaries in the surface-based variational model.