This paper presents a fibre-beam-element based model to capture the progressive collapse mechanisms of reinforced concrete (RC) frames. The model is comprised of rectangular and T-section fibre-beam elements. A stress-strain relationship for the steel which considers the embedment of the reinforcing bars in the concrete, the effect of concrete confinement and the bond-slip between the concrete and reinforcements are also considered in the model. The accuracy of the model is verified against experimental tests performed on two asymmetric one-story beam-column specimens with flange slabs under different lateral restraints. The first specimen, referred to as “OP”, was a two-bay frame subjected to a penultimate column removal scenario, while the other one, referred to as “OA”, was a three-bay frame with an antepenult removal scenario. The simulation results agree well with the experimental results with prediction of the peak capacity being within 10%. The model is then used to gain an in-depth understanding of the failure mechanisms of the two tested specimens. Numerical results reveal that the progressive collapse resistance of the RC frames is primarily determined by the bending stiffness and capacity of the columns. Compared to OP, the extra bay in OA provided a larger horizontal restraint to the damaged beam-flange slab, leading to 115% and 650% larger axial forces at the peak resistances under the stages of compressive arch action (CAA) and catenary action (CA), respectively. Furthermore, the penultimate column in OA was found to damage prior to its edge column, owing to its close proximity to the missing column and the additional bending moment MF generated by the redistributed axial forces to the columns.