Abstract: The influence of the surrounding rock weight on the rock stress around a shallow buried pipe can not be neglected. Based on the solution method proposed by Verruijt, with both the deadweight and the internal pressure considered, the surrounding rock stress in a semi-infinite region with a circular cavity is studied. The analytical solution of this problem by using complex functions, conformal mapping and Fourier transforms is obtained. The influence of the internal pressure and the radius and the ratio of the radius to the depth on the stress of the surrounding rock with consideration of the internal pressure and the deadweight is analyzed, which provides a theoretical basis for the pipeline design and the construction safety.