Compressive arch action (CAA) is a favourable structural mechanism to mitigate progressive collapse of reinforced concrete (RC) frames. To quickly and accurately predict the CAA capacity of RC sub-assemblages under a column-missing scenario, an engineering analytical model is proposed. The model considers all the design parameters in beams and the imperfect boundary conditions of sub-assemblages, including partial axial and rotational restraints, and connection gaps at beam ends if any. The proposed model is then validated with experimental results and extended to calculate progressive collapse resistance due to CAA with dynamic increase factors. Finally, the model is employed in parametric studies. It is found that CAA capacity increases with restraint stiffness only in the regime of weak restraints; in the regime of strong restraints, CAA capacity is not sensitive to variation in restraint stiffness. Furthermore, CAA enhances structural resistance more evidently for sub-assemblages with small span-to-depth ratios and low mechanical reinforcement ratios, and RC slabs help to increase the CAA capacities of RC frames.