The paper discusses the key stages of developing an integrated methodology for predicting the stress-strain state of a sand-polymer mandrel-plastic shell system during heat treatment with the adaptation of experimentally determined viscoelastic characteristics of components in the CAE ANSYS Mechanical APDL package. The first stage solves the problem of determining the effective viscoelastic characteristics for the shell. Viscoelastic characteristics are determined on the basis of the developed complex experimental calculation method based on the solution of boundary quasistatic problems of thermomechanics on a representative volume at two scale levels. The results obtained in this work, based on experimental data and developed numerical methods for determining the thermo-viscoelastic characteristics of composites, make it possible to estimate the contribution of stress relaxation in the mandrel and the shell to the evolution of the stress-strain state in the process of manufacturing the shell. Also, the developed technique makes it possible to predict the appearance of technological defects and determine the stages of heat treatment at which these defects occur.