In this paper, a solution of the problem of direct martensite transitions (DT) in a beam of a solid rectangular cross section from shape memory alloy (SMA) under the constant bending moment was obtained. An account has been taken of the property of the tension-compression asymmetry (TCA) of the SMA, which consists in a significant discrepancy between the stress-strain curves under tension and compression of samples from the SMA. The solution is obtained database on the model of nonlinear deformation of the SMA in phase and structural transitions in a single coupled thermomechanical formulation. An account has been taken of the heterogeneous hardening of elementary volume of SMA in DT. Slow processes are considered – the distribution of the temperature field over the height of the beam section is considered uniform. The Bernoulli-Euler hypotheses were accepted on the physical side of the beam bending process. Within the framework of the considered process, DT shows the effect of TCA of the SMA in compression and tension on the distribution of normal stresses and the phase composition parameter in the beam section, on the position of the boundaries of the beginning and ending of the phase transition in the stretched and compressed regions of the beam, and on the compliance of the beam. The position of the neutral plane at each point of the DT process is established. The influence of taking into account both homogeneous and heterogeneous hardening of the elementary volume of the SMA on the solution of the problem is shown. The range of values of the bending moment is determined, for which the influence on the solution of the problem of the phenomena of TCA and inhomogeneity of the hardening of the representative SMA volume during the DT turns out to be maximum. The convergence of the solution of the DT problem in the beam from SMA under a constant bending moment in a coupled formulation to the solution of a similar problem in a non-coupled formulation is shown.