In　practical　engineering,　the　concrete　structures　are　usually　subjected　to　an　initial　static　load　before　dynamic　loading.　Most　previous　studies　on　the　strain　rate　effect　of　concrete　do　not　consider　the　influence　of　initial　static　load　on　the　dynamic　strength,　which　leads　to　the　computed　results　of　dynamic　strength　larger　than　the　actual　value.　Therefore　the　structural　designed　by　these　methods　is　unsafe.　Based　on　the　mechanism　analysis　of　concrete　rate　effect　under　staticdynamic　coupled　loading,　a　clear　definition　of　initial　static　load　was　given　by　authors.　Then,　the　relationship　of　concrete　material　parameters　with　the　initial　static　load　and　the　strain　rate　was　derived.　And,　a　general　method　for　static-dynamic　coupled　strength　criterion　was　proposed.　The　combination　influence　of　initial　static　load　and　strain　rate　on　concrete　strength　is　reflected　by　the　strength　parameter.　The　static-dynamic　strength　of　concrete　is　consist　of　the　initial　static　load,　the　dynamic　cohesive　strength　and　the　frictional　strength.　Then　a　static-dynamic　coupled　multiaxial　strength　criterion　of　concrete　was　established　by　combining　the　obtained　concrete　material　parameters　with　nonlinear　dynamic　multiaxial　strength　criterion.　The　strength　surface　of　the　present　strength　criterion　expands　outward　with　the　increase　of　strain　rate　under　the　same　initial　static　load,　while　contracts　inward　with　the　increase　of　initial　static　load　under　the　same　strain　rate.　In　another　word,　the　strength　of　concrete　increases　with　the　increase　of　strain　rate　at　the　same　initial　static　load,　and　decreases　with　the　increase　of　initial　static　load　at　the　same　strain　rate.　Moreover,　when　the　initial　static　load　and　the　strain　rate　are　invariable,　the　strength　surface　of　this　criterion　is　determined,　and　the　loading　path　has　no　influence　on　the　strain　rate　effect　of　concrete,　but　the　hydrostatic　pressure　effect　is　influenced　by　the　loading　path.　Thus,　the　strength　of　concrete　at　different　loading　path　is　different　due　to　the　various　hydrostatic　pressure　effect.　Finally,　the　established　criterion　was　verified　based　on　the　static　and　dynamic　combined　strength　test　results　of　concrete.　©　2017,　Editorial　Office　of　Chinese　Journal　of　Theoretical　and　Applied　Mechanics.　All　right　reserved.