The obvious anisotropy of layered rock mass prevents the built-in constitutive model of commercial simulation software from accurately describing the elastoplastic behavior of the rock mass. In this paper, a transversely isotropic elastoplastic constitutive model (called the AN-MC model) that characterizes the elastoplastic failure behavior of the layered rock mass is developed by introducing the Mohr-Coulomb yield criterion with the tension cutoff in the model based on the transversely isotropic constitutive model and deriving its finite difference scheme. The development and programming of the transversely isotropic elastoplastic constitutive model are achieved on the basis of the secondary development platform of FLAC3D and the VC++ environment. The accuracy and rationality of the proposed constitutive model are verified in terms of consistency of the calculation results of the developed transversely isotropic elastoplastic constitutive model and the built-in constitutive models. In the numerical analysis of the Queerxi tunnel project, the calculation results of the AN-MC model are in good agreement with the field monitoring data. Thus, the deformation characteristics of the tunnel surrounding rock are well characterized. Comparative analysis of the deformation and failure laws of the layered surrounding rock and isotropic surrounding rock indicates that the plastic failure range of the layered surrounding rock tunnel is larger, and the arch foot and waist are prone to plastic penetration failure with butterfly-shaped characteristics. The research results are important for the scientific prediction and precise support of layered rock mass deformation.