Strain-rate　sensitivity　exists　in　concrete　subjected　to　dynamic　loads.　The　establishment　of　a　tri-axial　dynamic　strength　criterion　for　concrete,　therefore,　is　a　significant　effort.　Based　on　the　Generalized　Non-linear　Strength　Theory　combined　with　nonlinear　uniaxial　and　biaxial　dynamic　strength　criteria　of　concrete,　the　rate　effect　relation　of　strength　parameter　is　deduced.　Subsequently,　a　tri-axial　dynamic　strength　criterion　for　concrete　is　built.　Compared　with　biaxial　test　data,　the　results　show　that　the　dynamic　strength　criterion　accords　with　test　data　well.　The　non-linear　tri-axial　dynamic　strength　characteristics　of　concrete　are　analyzed　based　on　strength　parameters　of　concrete　material.