In nature, many rocks have a laminated structure, including shale, slates, gneisses, phyllites, and schists. It has been revealed through laboratory experiments that the strength of laminated rocks is dependent on the bedding plane orientation in the specimen, varying in a highly nonlinear fashion. To properly characterize the strength anisotropy of laminated rocks, various scholars idealized laminated rocks as transversely isotropic continua and developed the corresponding constitutive models and failure criteria satisfying the material symmetry requirement. Such a modeling scheme, however, is not applicable for laminated rocks with weakly cemented bedding planes, where the bedding structure not only makes the rock matrix behave as a transversely isotropic material, but also introduces a weaker plane orientation on which failure is easier to occur. Realizing this issue, we introduced a modeling scheme for laminated rocks where on top of the aforementioned model for failure through the rock matrix, we introduced a distinct failure model for failure along the bedding planes. Based on this concept, we developed models to characterize both the tensile strength and the shear strength of laminated rocks, and the proposed models can perfectly capture strength anisotropy as well as the orientation of localized failure for laminated rocks.