The　existing　test　results　and　semi-empirical　equations　of　the　rate-dependent　concrete　strength　have　overestimated　the　actual　dynamic　strength　because　they　do　not　distinguish　between　the　actual　dynamic　strength　related　to　the　strain　rate　effects　and　the　additional　resistance　caused　by　inertial　effects.　However,　an　ultimate　strength　of　concrete　exists　at　a　strain　rate　exceeding　a　certain　value.　This　paper　proposes　a　nonlinear　dynamic　uniaxial　strength　criterion　for　concrete　based　on　an　analysis　of　the　physical　mechanisms　governing　the　strain-rate-dependent　behavior　of　concrete　strength.　The　proposed　criterion　is　able　to　describe　the　actual　dynamic　strength　and　to　reflect　the　ultimate　strength　at　a　high　strain　rate　of　concrete.　The　results　from　two　groups　of　dynamic　uniaxial　compressive　tests　and　two　groups　of　dynamic　uniaxial　tensile　tests　are　used　to　verify　the　criterion.　Moreover,　the　recommended　physical　parameters　in　the　criterion　are　obtained　by　analyzing　the　statistical　test　results　of　dynamic　uniaxial　compression　and　tension.　The　recommended　parameters　can　be　used　in　the　criterion　to　study　the　dynamic　strength　of　concrete　when　dynamic　tests　are　not　feasible,　and　to　predict　the　dynamic　strength　at　high　strain　rates　when　tests　are　performed　at　lower　strain　rates.　(C)　2017　Elsevier　Ltd.　All　rights　reserved