Short columns may enter their plastic deformation range
before buckling occurs. The work-hardening of the
material during plastic deformation requires the load causing the deformation to increase and the column may then buckle in its plastic range. This process is known as inelastic buckling. The photograph illustrates this for a hollow tubular column with thin walls. Such a structure is used as an energy absorber for automotive crash protection.

In applying Euler modeling to this case it is the Tangent
Modulus at the buckling strain that determines the critical buckling stress. The tangent modulus decreases as the plastic strain increases, and is much less than Young's modulus for the material. The Inelastic Buckling stress, therefore, falls below the critical buckling stress predicted by Euler's elastic buckling model.