As opposed to slender columns, tubular members used in the automobile industry are quite “stocky” so that the shear rigidity is comparable to the bending rigidity. It has been conjunctured that appreciable shear forces developed in the process of progressive crushing might be responsible for a loss of stability and a global collapse of compressive members. This problem is studied here using a simple model of the tube undergoing finite rotations and local crushing. It was found that the shear forces are caused by redistribution of stresses at the crushed zones and tube ends and by the associated finite changes of the geometry of the tube. An essential mechanism which triggers these events is the unsymmetric local folding, described by Abramowicz and Jones.A simple estimate is given on the maximum magnitude of shear forces both in the positive and negative direction. At the level of a single compressed member, the global collapse can be prevented by controlling the local folding process. In the case of an integrated front panel, the unsymmetric folding of one member does not necessarily lead to a destructive global collapse. Often other members provide for the necessary restoring shear and bending force to resist the overall collapse.