In order to simultaneously describe the elasto-plastic and damage behaviors of rock-like materials under various pressure conditions, a 2D and 3D nonlocal hybrid elasto-plastic model based on Hoek-Brown criterion and generalized Zhang-Zhu (GZZ) criterion is proposed in this paper. The proposed model couples the nonlocal differential operator method (NDO) and the non-ordinary state-based peridynamics (NOSBPD) method to eliminate the surface effect arising from the incomplete integral region near the boundary. Additionally, this coupling simplifies the imposition of boundary conditions. A plastic constitutive model with the well-known Hoek-Brown criterion or GZZ criterion is integrated within this framework to accurately capture the nonlinear behavior of rock-like materials. Note, that the effect of intermediate principal stress on elastic-plastic fracture behavior is considered in the 3D model. The segmented flow rule is used for different pressure conditions. Strain-softening and fracture criteria, utilizing the equivalent plastic strain, effectively capture the elasto-plastic response and damage-fracture process in rock materials. The dynamic relaxation method and return mapping method are used for numerical calculations. Numerical examples contain the triaxial compression tests and compression tests of rock specimens with pre-existing flaws. Based on numerical examples, it has been effectively demonstrated that the model proposed in this paper can simulate the progressive failure process of rock-like materials from elastic-plastic deformation to strain softening and fracture.