Eighty-four dynamic tests on thin-walled square steel tubes having two different cross-sections with c/h = 30.25 and c/h = 32.18 and various lengths were crushed axially on a drop hammer rig. Approximate theoretical predictions were developed for the axial progressive crushing of square box columns using a kinematically admissible method of analysis. This theoretical study predicts four deformation modes which govern the behaviour for different ranges of the parameter c/h. New asymmetric deformation modes were predicted theoretically and confirmed in the experimental tests. These asymmetric modes cause an inclination of a column which could lead to collapse in the sense of Euler even for relatively short columns. The effective crushing distance is considered in the approximate theoretical analysis together with the influence of material strain rate sensitivity, which is important for steel even when the loadings are quasi-static. The simple equations presented herein for the design of axially crushed spuare box columns give reasonable agreement with the corresponding experimental results.