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Abstract Tunnels are becoming more popular in the transportation system, which makes it imperative to study the surrounding soil tunnel stability. However, in previous studies, researchers generally regarded soil as an isotropic and homogeneous material, which is not consistent with real conditions. Therefore, on the basis of the upper bound theorem, the influence of the anisotropy and non-homogeneity of soil on the earth pressure and the failure mechanism of shallow square tunnels is studied in this paper. The failure mechanism of the surrounding soil for excavation tunnel is obtained using a discrete technique. Considering the anisotropy and non-homogeneity of soil, the earth pressure formula is derived and the optimal solution is obtained. Compared to other results, it is shown that the present approach is feasible and effective. In addition, taking the tunnel of Daganxi II, Longyong expressway of Hunan province as an example, a numerical calculation is conducted, in which the displacement field corresponds to the theoretical one proposed in this paper. After discussing the impact of the anisotropy and the non-homogeneity of soil on earth pressure, the tunnel stability is studied with the presence of the pore water pressure. The effect of pore water pressure and the change of the water table level are then investigated. [ABSTRACT FROM AUTHOR]