Post-punching resistance of a flat slab can help redistribute the gravity loads and resist progressive collapse of a structure following initial damage. One important difficulty with accounting for the post-punching strength of a slab is the discontinuity that develops following punching shear. A numerical simulation technique is proposed here to model and evaluate post-punching resistance of flat slabs. It is demonstrated that the simulation results of punching shear and post-punching response of the model of a slab on a single column are in good agreement with corresponding experimental data. It is also shown that progressive collapse due to a column removal (explosion) can lead to punching failure over an adjacent column. Such failure can propagate throughout the structure leading to the progressive collapse of the structure. Through post-punching modeling of the slab and accounting for the associated discontinuity, it is also demonstrated that the presence of an adequate amount of integrity reinforcement can provide an alternative load path and help resist progressive collapse.