Abstract: The elastic complex function theory is used to simplify the shallow-buried subsea tunnel into a semi-infinite plane problem. The stress distribution of surrounding rock after tunnel excavation is explored considering the effects of self-weight of surrounding rock and sea water pressure. The fractal mapping function is used to map the surrounding rock domain to a circular domain like a plane, and the complex potential single-value analytical function is expanded to a Laurent series in the circular domain. The power term of Laurent series is determined by using the stress boundedness at infinite distances. The iteration expression of Laurent series coefficient is obtained according to the surface boundary and the non-uniform stress boundary condition at the orifice. The determined Laurent series condition is substituted into the iteration expression to obtain the explicit solution of complex potential function, thus realizing the iteration of complex potential function coefficient from low power to high power. According to the complex function expression of the stress component, the stress component of all points around the tunnel can be obtained. The influence of two single-value analytical functions with different powers on the results is studied, and the influence of buried depth of shallow tunnel on the toroidal compressive stress is analyzed. The results show that the power series solution has high reliability, and it agrees well with the finite element solution in the first half of the tunnel. The final calculation results of power series solution in the second half of the tunnel are relatively conservative compared with the finite element results. Sufficient numbers of complex potential functions are required to ensure the accuracy of calculation results. As the buried depth of the tunnel increases, the circumferential compressive stress at the bottom of the tunnel and at the waist of the holes on both sides increases continuously. The difference in circumferential stress between the lumbar and the bottom increases as well.