A phenomenon of instability of any load carrying structural element can be analyzed more in detail only when using a nonlinear approach. When analyzing columns, the approach based on a concept of inextensibility of axis is assumed to be perfectly good. It provides approaches to linearize the problem of stability, since the stability loss of real bars usually is of a bifurcation type. However, there are cases when the shortening (elongation) of elastic axis of a column should be accounted for. When analyzing global stability of such structural elements as bellows or springs, which are represented by some equivalent column with the reduced stiffness characteristics, the effect of the axis shortening should be taken into account. We study a supercritical deformation of elastic column with inextensible axis in geometrically nonlinear statement. We analyze two possible models of deformation of such a column and obtain exact solutions for both of them. Based on these solutions, we provide particular numerical calculations, the results of which reveal some interesting peculiarities of the supercritical deformation. It is proven that the stability loss of a column with a highly compressible axis can be of a not bifurcation type.