The work is devoted to numerical modeling of the process of еxpansion and compression of a thick-walled cylindrical shell made of a shape memory alloy (SMA) in the martensitic inelasticity mode. The processes of expansion and compression occur under the influence of monotonically increasing internal or external pressures. The problem is considered within the framework of the model of nonlinear deformation of SMA in phase and structural transformations. The resulting solution takes into account tension-compression asymmetry of these alloys. The solution is obtained for cases of plane-stress and plane-strain states. Numerical modeling was performed in the Simulia Abaqus using user material technology. The parameter associated with the third invariant of the stress deviator is used as a parameter of the type of stress state. In the framework of the work, a linear dependence of material constants on the type parameter of the stress state is taken. The distribution and compression of a thick-walled cylindrical shell was simulated in a three-dimensionally space-based formulation, taking into account the symmetry of the problem. In the framework of the work, stress diagrams were obtained over the shell cross section for various pressure values. It was established that during loading the stresses across the cross section change nonmonotonically, and the stress distribution itself has a nonlinear dependence on the radius. For both cases of pressure, the parameter of the type of stress state has an inhomogeneous distribution over the cross section of the shell. The dependence of the displacements of points on the inner and outer shell surfaces from the value of the applied pressure is also obtained. The results obtained during the work can be successfully used in the design of thermomechanical couplings from SMA.