In this contribution, we present a recently developed optimization framework for the shear strength reduction method (SSRM). The optimization approach is built on Davis' approximations, enables to define lower and upper bound theorems of SSRM or find more advanced discretization and numerical methods. Next, we focus on a relationship between factors of safety (FoS) determined by the limit analysis and the SSRM methods and show the corresponding theoretical results. A solution concept based on a regularization, the continuation Newton method and mesh adaptivity is presented. Finally, the theoretical results are illustrated on numerical examples related to stability of slopes with and without seepage.