The work is devoted to the numerical simulation of direct martensite transformation (DMT) in shape memory alloys (SMA) taking into account tension-compression asymmetry. Uunder 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 DMT is performed using the finite element method. A model of nonlinear deformation of the SMA during phase and structural transformations was used as a material model. In this work, a velocity stiffness matrix corresponding to the process of cooling a sample from an SMA through the temperature range of the DMT was obtained. The velocity stiffness matrix obtained in this work takes into account the variability of the elastic modules of the SMA during the phase transition and the dependence of the accumulated phase strain during cooling on the magnitude of the acting stress. The cooling process is considered in a coupled formulation, taking into account the effect of the acting stress on the values of the direct transformation temperatures. The verification of the user material model is carried out based on an analytical solution to the problem of a beam made of an SMA under a constant tension stress and undergoing cooling through the temperature range of the DMT. In the framework of this work, the calculation of the stress-strain state of a spherical thick-walled SMA shell under the action of constant internal or external pressure during its cooling through the temperatures of the DMT was performed. It was found that during the cooling of the shell under the action of constant internal or external pressure, the stress state parameter does not depend on the radial coordinate of the shell. In the case of the action of internal pressure, the parameter of the type of the stress state corresponds to the case of pure compression, with the action of external pressure, to pure tension.