An　explicit　strength　criterion　for　rock　is　proposed　which　is　based　on　the　parameter　of　the　product　of　intermediate　and　minimum　principal　stresses　(σ2σ3).　This　criterion　consists　of　two　parts:the　skeleton　curve　which　is　the　results　of　triaxial　compression　tests,　and　the　branch　curve　which　is　the　results　when　the　minimum　stress　is　fixed.　By　studying　the　results　of　true　triaxial　compression　experiments　of　rocks,　a　strong　correlation　between　the　failure　strength　of　the　rock　and　the　square　root　of　the　product　of　intermediate　and　minimum　principal　stresses　(√σ2σ3)1/2)　is　observed.　The　slopes　of　the　skeleton　curve　and　the　branch　curve　are　equal　at　the　intersection　in　this　coordinate　system.　Based　on　this　observation,　the　slope　of　skeleton　curve　is　found　two　times　of　the　slope　of　the　branch　curve　at　the　intersection　in　the　maximum　principal　stress　and　intermediate　principal　stress　plane.　It　is　observed　that　the　failure　strength　for　a　rock　always　reaches　a　maximum　value　as　the　difference　between　intermediate　principal　stress　and　minimum　principal　stress　is　a　constant　value　in　all　branch　curves.　According　to　the　above　characteristics　of　rocks,　the　functions　of　skeleton　and　branch　curves　are　derived.　The　proposed　criterion　is　validated　by　experimental　data　and　compared　with　other　criteria.　The　results　show　that　the　proposed　failure　strength　criterion　for　rock　can　fit　the　triaxial　failure　strength　of　rock　material　well.　This　criterion　can　also　fit　relatively　stable　and　accurate　results　with　even　less　data.　©　2022,　The　Editorial　Board　of　Journal　of　Basic　Science　and　Engineering.　All　right　reserved.