This research presents the modernization of a method for selecting design solutions based on the key parameters of interference-fits through mathematical modeling. It provides practical recommendations for engineering applications. Based on the analysis of numerical and analytical methods used in the automated design of interference-fits, a multiparametric set of mathematical models was developed to define the domain of feasible design solutions (valid fits). This comprehensive model is represented by a set of three-dimensional geometric entities, one of which – a fragmentary model – is the focus of this research. The influence of key parameters: Specific Contact Pressure, Fitting Working Length, and Fitting Diameter on the magnitude of the Interference, that directly affects the quality and reliability of the joint, is analyzed. An analytical approach based on the theory of R-functions is used to describe spatial models of shrink-fit assemblies during thermal joining. Software tools were developed for numerical analysis and automated design. The resulting numerical-analytical models can be integrated into CAE/CAD/CAM environments to improve the accuracy and efficiency of interference-fit design.