A　differential　equation　is　proposed　to　express　the　relationship　between　dynamic　increasing　factor　of　strength　increasing　amplitude　and　logarithm　strain　rate　of　concrete　based　on　experimental　results　of　uniaxial　dynamic　strength　tests.　On　this　basis,　a　non-linear　uniaxial　dynamic　strength　criterion　of　concrete,　namely　J　criterion　is　established.　Furthermore,　a　maximum　dynamic　increasing　factor　of　strength　increasing　amplitude　for　improving　the　J　criterion　to　transform　into　a　new　criterion,　namely　S　criterion,　to　describe　the　dynamic　peak　strength　characteristics　of　concrete　is　introduced.　The　validity　of　the　J　criterion　and　S　criterion　are　verified　by　published　results　of　uniaxial　dynamic　strength　tests　of　concrete.　Comparing　with　the　bilinear　uniaxial　dynamic　strength　criterion,　the　J　criterion　and　the　S　criterion　are　able　to　satisfactorily　describe　the　nonlinear　dynamic　strength　characteristics　of　concrete.　Both　criteria　have　fewer　parameters,　unified　expression　and　continuous　smooth　strength　curve,　and　the　S　criterion　is　able　to　reflect　the　uniaxial　dynamic　limit　strength　of　concrete.