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After testing according to the developed state methods and procedures for polyurethane foam thermal insulation of laminated composite structures with metal facings, the issues of correlation, probabilistic-statistical regression models between the signs of elasticity in tension Eshear and signs of elasticity in shear Gshear were investigated. It is shown that the test results are random stochastic values. Their variability, depending on the type of tests and the parameter under study, is in the acceptable average values. The presence of a significant number of each of the characteristics, for example, Eshear - Gshift, predetermined the use of correlation tables to establish the fact of a relationship. Modules of elasticity under tension and shear were determined. The correlation coefficient between Eshear and Gshift is 0.659. With the help of a computer program, correlation tables were built and the calculation of the probabilistic-statistical interaction of characteristics with different reference points was made. When considering one-dimensional aggregates, the laws of distribution of positive values of the characteristics of foams can be adopted of various types. The connection between phenomena can be not only linear, but also non-linear. In this case, nonlinear correlation can be realized in the form of parabolic and other equations of a certain degree. The calculation of the interaction is carried out on the basis of second-order parabolic equations. Approximation in the form of second-order equations does not greatly improve the convergence, but the possibilities for extrapolating statistical models are reduced.