The　dynamic　responses　of　the　structure　are　different　when　the　ground　motions　generate　along　different　directions　as　excitations,　and　there　exits　a　critical　angle　to　attain　the　maximum　response.　The　critical　angle　calculated　based　on　traditional　method　is　a　horizontal　angle　because　only　the　two-component　ground　motions　in　the　plane　are　considered,　and　the　adverse　effect　of　the　vertical　ground　motion　is　not　concerned.　The　common　mechanism　between　maximum　principal　stress　direction　in　elastic　mechanics　analysis　and　the　critical　angle　of　structure　in　the　plane　is　demonstrated.　The　expression　of　maximum　principal　stress　direction　in　the　space　is　derived　and　the　formula　of　the　structure　critical　angle　for　three-dimensional　ground　motions　is　proposed.　The　calculation　method　of　the　three-dimensional　critical　angle　for　inelastic　structure　in　three-dimensional　ground　motions　is　presented　based　on　nonlinear　finite　element　analysis.　The　characteristics　and　regularity　of　the　critical　angle　in　three-dimensional　ground　motions　is　discussed　based　on　numerical　modeling.　It　is　proved　that　the　three-component　seismic　motion　and　the　corresponding　critical　angle　should　be　calculated　for　the　structure　has　obvious　vertical　modal　shapes,　and　the　critical　angle　of　the　inelastic　structure　is　transient　and　is　related　to　the　structural　damage　degree.　©　2016,　Nanjing　University　of　Aeronautics　an　Astronautics.　All　right　reserved.