In the work, an analytical solution of the problem on the stress-strain state (SSS) of a thin-walled sphere and a cylinder of a shape memory alloy (SMA), which is under the influence of internal or external pressure, is loaded in the mode of martensitic inelasticity (MN) or in the process direct transformation without taking into account elastic deformations and taking into account 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. In the framework of the work, a linear dependence of material constants on the type parameter of the stress state is taken. 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 on the distribution (compression) of thin-walled structures is demonstrated. The distribution and compression of thin-walled structures are simulated taking into account axial symmetry. Thin-walled cylinders are considered under the assumption of plane deformation (PD) and plane stress state (PSS). It has been established that the parameter of the state of stress of a thin-walled cylinder under the assumption of PD is the same as under pure shear, both under internal and external pressure, and under the assumption of PSS, it is the same as under uniaxial tension at internal pressure and uniaxial compression at external . It was established that under the same loading (internal or external pressure), the parameter of the state of stress for a thin-walled sphere and a thin-walled cylinder has different values.