In the work, a numerical solution of the problem on the stress-strain state (SSS) of a thick-walled sphere made of a shape memory alloy (SMA), which is under the influence of constant internal or external pressure in the mode of martensitic inelasticity (MI) taking into account elastic deformations and the property of material tension-compression asymmetry. Under the property, tension-compression asymmetry refers to the dependence of the material constants of these alloys on the type parameter of the state of stress. The parameter associated with the third invariant of the stress deviator is used as a parameter of the type of stress state. The solution was obtained on the basis of the model of nonlinear deformation of SMA during phase and structural transformations. When solving the problem without taking into account elastic deformations, the provision on active processes of proportional loading is used. In the framework of the deformation process under consideration, the influence of the SMA diversity resistance as well as elastic deformations on the distribution of radial and ring stresses in the sphere cross section is demonstrated. It has been established that the distribution of radial and circular stresses over the sphere cross section is nonlinear, and the stresses themselves can vary nonmonotonously during loading. In the course of work, the module of the finite element complex Simulia Abaqus was verified, which was developed for the analysis of the SSS of structures from SMA in the MI mode. As a verification basis, the obtained numerical solution of the spatial three-dimensional boundary-value problem of SSS of a thick-walled spherical shell made of SMA under the loading of internal or external pressure, taking into account the different resistance of these alloys, was used. The obtained numerical solution converges to the analytical solution of the corresponding problem without taking into account elastic deformations with increasing of Young’s modulus.