In this paper, a layer-by-layer removal model of surface atoms (Al) is established according to the atomic structure of sapphire, which can accurately calculate etch rates of crystal planes and analyze the anisotropy of etch rates of sapphire. Firstly, etch rate distributions of sapphire are gained through different etching experiments of sapphire hemispheres, and the effect of concentrations of the etching solution on etch rate distributions are analyzed. Then, different types of surface atoms are classified based on the types of chemical bonds of surface atoms, the arrangement laws of surface atoms of different crystal planes are analyzed and a general formula for calculating etch rates of different planes is proposed. Finally, the effectiveness of the layer-by-layer removal model of surface atoms (Al) is proved by small errors between calculated rates of the model and experimental rates at different concentrations, and the factors affecting the anisotropy of etch rates of sapphire are summarized, which include: (1) the vertical distances between two adjacent layers of surface atoms of crystal planes; (2) the configurations of the types of surface atoms of crystal planes.