Establishing　a　concise　and　accurate　analytical　model　is　the　key　to　developing　a　feasible　progressive　collapse　design　for　engineering　practice.　However,　existing　models　either　focused　on　an　individual　force　mechanism　or　required　complicated　computer　programming.　Among　existing　machine　learning　(ML)　techniques,　multi-gene　genetic　programming　(MGGP)　can　be　trained　to　obtain　explicit　formulas　for　engineering　problems.　In　this　study,　a　comprehensive　database　was　established　by　data　collection,　Latin　hypercube　sampling　and　structural　design,　and　was　used　to　train　the　mathematical　model　for　quantifying　progressive　collapse　resistance　of　reinforced　concrete　(RC)　beam-column　substructures　under　middle　column　removal　scenarios.　Further,　an　energy-based　error　index　was　proposed　to　validate　the　accuracy　of　the　MGGP　model　among　others.　The　research　outcomes　can　provide　references　for　the　development　of　simplified　analytical　models　for　calculating　the　progressive　collapse　progress　of　RC　frame　structures,　and　promote　the　development　of　the　practical　design　method.　©　2023　World　Scientific　Publishing　Company.