A structure’s material plasticity influence on the pattern of contact interaction of its elements during operation is studied. The stress-strain state problem for the inner casing of a steam turbine high-pressure cylinder operating at supercritical steam parameters (over 240 atm and 565 °C) is solved. The problem is solved by using a finite-element software package. A model of thermoplasticity with kinematic and isotropic hardening is considered. In carrying out the study, experimental strain curves were used for the materials of the connection. The main dependencies used in solving the problem are given. The method of solving the thermal contact problem of interaction of flange connector elements in the conditions of plasticity is based on the application of a contact layer model. To be able to take into account changes in the load from the fastening in the process of combined strain of both the fastening and the casing, first proposed is a method of the three-dimensional modeling of the thermal tightening of the fastening of the horizontal casing connector by applying the linear coefficient of linear expansion of the material. The proposed approach allows modeling the stress of the initial tightening of studs by specifying a fictitious change (decrease) of the coefficient of linear expansion of a stud given as a separate body in the calculation scheme. The magnitude of the specified change in the coefficient of linear expansion is determined from the relationship between the stress of the initial tightening in the stud and the required, for its creation, elongation, which is implemented in the calculation scheme in the presence of different values of linear expansion of both the stud and the casing. To conduct the numerical experiment, an ordered finite-element grid of the casing design was constructed. A 20-node finite element was used in the construction of the casing grid and the fastening. The effect of force loads and the temperature field, in which the structural element under consideration is operated, is taken into account. An analysis of the results of distribution of equivalent stresses and contact pressure during operation is carried out. The difference between the obtained results and the results of solving the problem in the elastic formulation is noted.