The work is devoted to the numerical analysis of the dorning process of a cylindrical coupling made of shape memory alloy (SMA) in the mode of martensitic inelasticity (MI). The problem is considered within the framework of the model of nonlinear deformation of the SMA during phase and structural transformations. The resulting solution takes into account both elastic deformations and the property of the material’s resistivity. The resistance of the materials is understood as the dependence of the material constants of these alloys on the parameter of the type of stress state. The parameter associated with the third invariant of the stress deviator is used as a parameter of the type of stress state. Numerical simulation was performed in the Simulia Abaqus software package using the technology of user-generated material. Modeling of the dorning process of a thick-walled cylindrical coupling is implemented using an iterative method in which the stress-strain state of the previous step is preserved at each step corresponding to the movement of the coupling for a given distance in the axial direction. The problem is solved in a three-dimensional formulation taking into account the axial symmetry of the coupling. As part of the work, stress diagrams were obtained along the coupling cross-section for each step corresponding to the position of the mandrel at a certain time. It is established that in the process of loading, the cross-section stresses change nonmonotonically, and the stress distribution itself has a nonlinear dependence on the radius. The parameter of the type of stress state also has an inhomogeneous distribution over the cross section of the shell. It is noticed that as the mandrel moves deeper into the coupling, the plot of axial stresses and the parameter of the type of stress state change along the section of the coupling. The results obtained in the course of the work can be successfully used in the design of thermomechanical coupling couplings from SMA.