A finite element (FE) modelling study on the progressive collapse of steel frames under a sudden column removal scenario is presented. The FE models were developed with refined shell elements using the general purpose FE software package ABAQUS. The FE models were first validated by comparing the predicted responses with the measured results from an experimental study on the progressive collapse of three steel frame specimens. A new bearing capacity-based index was introduced to quantify the robustness of the steel frames. The robustness index takes into account the dynamic effects and the plastic internal force redistribution. By incorporating the experimental results and the numerical simulations, the dynamic amplification factor in the progressive collapse of the steel frames was assessed. The validated FE models were further applied to identify the collapse modes of planar steel frames and evaluate the influences of a range of mechanical and geometrical parameters on the progressive collapse and the robustness. The results showed that, for a column-instability induced progressive collapse mode, the influences of the damping is larger than the influences of the strain rate of material on the robustness. However, for the connection-failure induced progressive collapse mode, the influences of the strain rate is larger than the damping. The type of the steel frame (e.g. weak-beam strong-column or vice versa) and the location of the column removal were both found to play an important role in influencing the critical load and the robustness of steel frames.