Using both physical and geometrical nonlinear approaches, we study a phenomenon of the loss of stability of one simplest mechanical system, a Shenly column. A Shenly column is a system of an absolutely rigid body and two rods made from a shape memory alloy. The rods may be compressed or stretched and may undergo thermo-elastic phase transformations not due to variations in temperature but due to change in stress-strain state only, that is, due to loading.