Shape memory alloys (SMAs) are used in many applications as actuators or fixed parts of complex structures. In both cases, they often function under the influence of variable temperatures and loads, which are often compressive. This leads to the need to analyze the stability of these elements. Due to the complex thermomechanical behavior of SMAs and the lack of a unified approach to describing their stress-strain state, stability calculation is significantly complicated even for objects with the simplest geometry. Due to the specified difficulties and the small number of papers devoted to this topic, an attempt was made to solve the problem of stability of one-dimensional loading, using the most complete model of the behavior of the SMAs. This work is devoted to the analytical study of the stability of the Shanley column on SMAs rods during reverse phase transformation under the action of a constant load. For the first time, a combined model of inelastic deformation of SMAs is used for such a task. Two methods of preparing rods before starting the reverse transformation are considered, namely, deformation in the mode of martensitic inelasticity and direct phase transformation under the action of a constant load. As a criterion for the loss of stability, the quasi-static Euler method is used, which allows linearizing kinematic constraints and static equilibrium equations, with respect to small angles of deviation of the Shanley column from the vertical position. The concepts of a fixed and variable external load are compared during the transition to an adjacent form of equilibrium. For the correctness of the formulation in the concept of a variable external load, a number of hypotheses are introduced regarding the order of smallness of the quantities that can receive increments during the loss of stability. Depending on taking into account the coupling between different state parameters during the transition to an adjacent form of equilibrium, the problem is considered in three statements: non-coupled, coupled with respect to stress increments, coupled both with respect to stress increments and thermomechanically.