Abstract Research challenges associated with progressive collapse of reinforced concrete (RC) structures have attracted growing attention from researchers and industries worldwide, since the 1995 explosion at the Murrah Federal Building in Oklahoma City. The compressive arch action (CAA), as a favorable mechanism to provide the structural resistance to progressive collapse under a column removal scenario, has been extensively studied using both experimental and theoretical approaches. However, the existing prediction models for the CAA resistance are either too complicated or in need of additional information like the peak deformation of the specimen. Another major weakness in the previous CAA calculation models is the negligence of the slab effect, which can contribute significantly to the structural resistance. In this study, based on the finite element analysis of 50 progressive collapse tests reported in the literature and 217 newly designed beam-slab substructures, explicit and easy-to-use CAA calculation models are developed for RC frame beams with and without slabs. The proposed models are validated against both experimental and numerical results with a mean absolute error being less than 10%. The findings from this study can serve to provide a quantitative reference for practical design of RC frame structures against progressive collapse.