The work is devoted to the numerical simulation of the phenomenon of martensitic inelasticity in shape memory alloys (SMA), taking into account their tension-compression asymmetry. Under tension-compression asymmetry is meant the dependence of the stress-strain state of these alloys on 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 of the process of martensitic inelasticity is carried out in the framework of the model of nonlinear deformation of SMA in phase and structural transformations. In the course of the work, the integration of relations describing the behavior of the SMA under monotonous active loading in the low-temperature martensitic phase into the finite-element complex of Simulia Abaqus was performed using the procedure for creating user material. For this purpose, relations are reversed that establish the relationship between the components of the tensors of total deformations and stresses in order to obtain a tangent stiffness matrix used as a physical law for each element of the model. The process of validation of the module, developed for the finite-element analysis of the stress-strain state of structures containing SMA, was performed using the available experimental data for uniaxial tension and compression of samples from these alloys. A comparison is made of the deformation diagrams obtained by finite-element modeling of the phenomenon of martensitic inelasticity in a three-dimensional in space formulation with experimental curves. As part of the work, the stress-strain state of a spherical thick-walled shell from SMA under the action of internal and external pressure was calculated. It was established that in the process of deformation of the shell by internal pressure for each element through the thickness of the shell, the parameter of the type of stress state takes on the value corresponding to pure compression, and for the case of external pressure, pure tension.