When selective pallet racks are allowed to rock in the cross-aisle direction during an earthquake, the uprights are subjected to short duration high axial forces at stomping. In this paper, the amplitude of the stomping force needed to compromise the upright's residual capacity is assessed for 59 configurations using nonlinear inelastic static and dynamic analyses. Parametric studies are performed to investigate the effects of upright length, bracing pitch, section slenderness, torsional restraints and multiple impulses on the residual capacity of an upright due to rocking. Uprights that fail in the flexural-torsional buckling mode perform better than those that fail by local-distortional buckling as the stomping causes permanent local-distortional deformations rather than sweep (torsional deformation). A rack upright that has a greater length, greater thickness and lower torsional restraint tends to have a higher residual capacity (relative to the undamaged capacity). A typical cold-formed steel rack upright can sustain a 0.1 s stomping force that is at least 15% greater than its static ultimate capacity without significant reduction in residual capacity. An implication is that an unanchored upright that survives an earthquake through rocking may double its storage load during the post-earthquake emergency period. The present shell element analysis results can be used to plan an experimental program for optimising the resilience of storage rack uprights against stomping.