In product design, tolerances are specified due to the inherent variabilities of manufacturing processes. Tolerance specifications have significant implications on the quality and cost of the product. For proper tolerance specification, tolerance analysis must be performed. Prototyping is the the only method available for the analysis of the product geometric variations. For the automation of the analysis procedure, the part tolerance information must be represented in a format suitable for computer interpretation. Previously proposed tolerance representation schemes have suffered either from inadequate variational coverage or departure from the established ANSI tolerancing standards. Toward this end, a tolerance representation scheme capable of modeling the range of tolerances defined in the ANSI Y14.5 standard in a format suitable for automated tolerance analysis has been proposed. One unique feature of this representation scheme is the use of B-splines for the modeling of form variations. The representation scheme can also take into account the distribution characteristics of the manufacturing processes used to enable statistical tolerance analysis. To provide an accurate characterization of the variational form characteristics of the manufactured part features, the use of process capability templates was introduced. For assembly tolerance analysis, a relative positioning scheme capable of modeling the interaction between mating splines was developed to propagate the individual part variations within the assembly. This enabled the tolerance stackup on the assembly design function(s) to be computed automatically without the need to formulate any tolerance functions. A prototype software, written in the C++ programming language and running from within CATIA, has been developed to demonstrate the integration of the above concepts. / Ph. D.