Stratified rock mass is a common rock mass structure and distributed widely on the earth’s crust. High-density distribution of stratified structural planes in the stratified rock mass has a great influence on the mechanics properties of the rock mass, such as anisotropy of stress and seepage. Therefore, anisotropy is the inherent characteristic that must be considered in the stratified rock mass as well as the stratified rock slope stability. According to the anisotropic characteristics of stratified rock mass, an anisotropic seepage-stress coupled model for the mechanical behavior of stratified rock slope is proposed based on the anisotropy elasticity theory. The model is validated by simulating seepage and stress fields of an idealized slope using the finite element method. The deformation and stress-dependent permeability of the slope are predicted and compared well with the previous study, thus confirming its capability in characterizing the response of rock slope that is dominantly affected by rock anisotropy. Finally, the model is used to simulate the anisotropic properties of a stratified rock slope of Fushun west open-pit mine, China. The simulation is in good agreement with the actual measurement, which means the proposed model is capable of simulating anisotropic properties of the stratified rock slope.