On an example of the rod from a shape memory alloy (SMA) is shown a propensity to buckling of thin-walled elements out of a shape memory alloy, being in a state of chaotic martensite and under loads, which able to cause a buckling. In framework of various approaches are received analytical solutions of the problem buckling of the rod from SMA, previously without a load transformed from an austenite state to a martensite state as a result of cooling through an interval of temperature of a direct martensite transition. Therefore, it is possible to consider that the material of the rod before loading is in a state of a chaotic martensite. Further the rod is subjected to quasistatic uniform incremented compression, which leads to accumulation of structural strains due to increase of a degree of directivity of a martensite and, at certain critical load, to the buckling. The analysis of the found solutions shows that the studied rod can buckle at values of a critical load, essentially smaller than the matching Euler’s force at the martensite value of elastic modulus SMA.