To　investigate　rock　slope　stability,　a　nonlinear　strength-reduction　numerical　manifold　method　(NSRNMM)　using　a　generalized　Hoek-Brown　(GHB)　criterion　is　proposed.　As　it　is　difficult　to　implement　the　nonlinear　strength　reduction　method　(NSRM)　with　the　use　of　the　GHB　criterion　by　directly　reducing　the　GHB　parameters,　two　equivalent　Mohr-Coulomb　(MC)　criteria,　namely,　the　instantaneous　and　average　equivalent　MC　criteria　that　are　derived　from　the　GHB　criterion,　are　adopted　in　the　NSRNMM.　The　implementation　details　of　the　NSRNMM　are　discussed.　The　stability　of　two　rock　slopes,　namely,　a　rock　slope　with　a　GHB　material　and　a　rock　slope　with　a　GHB　material　and　two　MC　materials,　is　investigated　using　the　NSRNMM.　The　numerical　results　indicate　that　1)　the　proposed　NSRNMM　using　the　instantaneous　equivalent　MC　criterion　can　accurately　calculate　the　safety　factor　(Fs)　of　rock　slopes　and　that　2)　the　Fs　predicted　with　the　NSRNMM　using　the　average　equivalent　MC　criterion　is　more　conservative　than　that　using　the　instantaneous　equivalent　MC　criterion.　©　2020　Elsevier　Ltd