The　classical　strength　criteria　including　Mohr-Coulomb　strength　theory,　Drucker-Prager　strength　theory,　Matsuoka-Nakai　strength　theory,　Lade-Duncan　strength　criterion　and　Hoek-Brown　strength　criterion　are　developed　into　dynamic　multiaxial　strength　criteria　by　deriving　the　strain-rate-dependent　strength　parameters　of　each　static　strength　criterion.　The　strain-rate-dependent　strength　parameters　are　obtained　by　combing　the　dynamic　uniaxial　S　criterion　and　the　basic　strength　indexes　of　concrete　material.　Then　the　change　rules　and　value　range　of　strength　parameters　of　five　strength　criteria　are　analyzed　by　these　statistical　material　parameters　of　S　criterion.　On　the　basis　of　the　uniaxial　compressive　and　tensile　strengths　of　concrete,　the　strength　curves　of　each　dynamic　multiaxial　strength　criterion　at　plane　stress　condition,　meridian　plane,　deviatoric　plane　and　the　strength　surfaces　in　the　principle　stress　space　are　given.　Then　the　differences　of　the　five　dynamic　multiaxial　strength　criteria　are　analyzed.　The　five　dynamic　strength　criteria　are　evaluated　by　the　dynamic　biaxial　and　true　triaxial　strength　tests.　The　dynamic　Drucker-Prager　criterion　shows　big　differences　with　the　dynamic　test　results　of　concrete.　All　of　the　dynamic　strength　criteria　are　able　to　reasonably　describe　the　strength　rules　under　biaxial　compression-tension.　It　also　shows　big　difference　among　these　dynamic　strength　criteria,　while　the　dynamic　Matsuoka-Nakai　criteria　describes　the　strength　rules　better　than　others.　Under　dynamic　true　triaxial　proportional　loading,　Mohr-Coulomb　and　Hoek-Brown　strength　criteria　cannot　consider　the　influences　of　intermediate　principal　stress,　while　the　Matsuoka-Nakai　and　Lade-Duncan　strength　criteria　are　capable　of　well　describing　the　test　results　of　concrete.　©　2016,　Editorial　Office　of　Chinese　Journal　of　Theoretical　and　Applied　Mechanics.　All　right　reserved.