It　is　well-known　that　the　responses　of　a　structure　are　different　when　subjected　to　a　static　load　or　a　sudden　step　load.　The　dynamic　amplification　factor　(DAF),　which　is　defined　as　the　ratio　of　the　amplitude　of　the　vibratory　response　to　the　static　response,　is　normally　used　to　depict　the　dynamic　effect.　For　a　single-degree-of-freedom　system　(SDOF)　subjected　to　a　sudden　dynamic　load,　the　maximum　value　of　DAF　is　2.　Many　design　guidelines　therefore　use　2　as　an　upper　bound　to　consider　the　dynamic　effect.　For　a　civil　engineering　structure,　which　is　normally　a　multiple-degrees-of-freedom　(MDOF)　system,　the　DAF　may　exceed　2　in　certain　circumstances.　The　adoption　of　2　as　the　upper　bond　as　suggested　by　the　design　guidelines　therefore　may　lead　to　unsafe　structural　design.　Very　limited　studies　systematically　investigate　the　DAF　of　a　MDOF　system.　This　study　theoretically　investigates　the　DAF　of　a　MDOF　system　when　it　is　subjected　to　a　step　load　based　on　the　fundamental　theory　of　structural　dynamics.　The　condition　on　which　the　DAF　may　exceed　2　is　defined.　Two　numerical　examples　and　one　experimental　study　of　a　cable-stayed　bridge　subjected　to　sudden　cable　loss　are　presented　to　illustrate　the　problem.　©　2020,　Institute　of　Engineering　Mechanics,　China　Earthquake　Administration.