There is an increasing trend of tunnel infrastructure construction in cold regions due to the advance of a western development strategy. To reduce the frost damage sustained by a tunnel, it is important to consider the mechanical properties of frost heave in the surrounding rock by analyzing the anisotropic frost heave of a cold-region tunnel. This paper elaborates on the behavior of anisotropic frost heave in the rock surrounding a cold-region tunnel, and the coefficient of displacement relief is adopted to indirectly quantify the influence of the tunnel construction process. The analytical elasto-plastic solutions of the stress and deformation in the surrounding rock are derived with Drucker-Prager criteria (hereinafter referred to as the D-P criteria) by modifying the constitutive equation for the frozen surrounding rock. Finally, an example is given to obtain the influence law of the distribution of stress and deformation in the surrounding rock. The results indicate that the plastic radius and frost force calculated by considering isotropic frost heave are greater than those obtained by considering anisotropic frost heave. The influence of the related parameters also analyzed. Some useful insights are provided for future numerical simulations and the design and construction of cold-region tunnels.