Abstract: This paper presents methods for calculating circular cavity expansion under a slope. The slope boundary is turned to be horizontal with a coordinate transformation technique. Using the complex variable method and mapping the hole and half-plane to a circular ring offer an analytical solution for stress, considering the initial gravity stress. When the circular cavity is deep enough, the influence of the ground surface is ignored and the problem is simplified as cavity expansion in an infinite space. Then, the solutions are attained by superposition of results from stress components. The radial stress, σ_r, hoop stress, σ_φ and shear stress, τ_rφ, are analyzed and the results show that the stresses at a certain point in a slope are affected by the slope dip and the distance from the cavity center. Specifically, with a distance from the cavity center greater than 4 times the cavity radius R, the stress caused by a cavity at a point can be safely neglected, which means the final value is close to original gravity stresses. Meanwhile, results calculated by superposition method for the deep cavity agree with those from complex variables method. At a point, specifically a distance of 2.5R from the cavity center, values of σ_r and σ_φ are all negative. However, the positive and negative values of τ_rφ are cross distributed. The distribution of stress extremum is related to the slope dip.