This paper describes a method that allows direct use of the Generalized Hoek-Brown criterion in Finite Element (FE) Shear Strength Reduction (SSR) analysis of rock slopes. It describes the generation of shear envelopes for the criterion, lowering of the shear envelope by a factor, and means for determining an equivalent Generalized Hoek-Brown curve that best approximates the lowered envelope. The paper provides two examples that demonstrate the performance of the new method. As well it outlines some of the benefits of the SSR technique for slope stability analysis.