The influence of destruction of a support on the loss of stability of an elastic column under compression is being investigated. There is dependence between external loading and moving of the mobile end of the column at every stage of deformation. It is shown that the column can keep sustaining ability after the loss of stability or durability damage in the support. The initially elastic, pliable support is exposed to partial destructions, owing to which its rigidity decreases. The process of the loss of stability of an absolutely rigid column with a failing support was taken under consideration in .