Considering the boundary and the surface conditions,the stress field and displacement field caused by the construction of the shallow rectangular pipe jacking are solved by the complex function method. According to the Riemann's existence theorem and basic complex variable theory,a conformal mapping function which can transform the half-plane with a rectangle cavity into the concentric ring is established. The both sides of boundary conditions equation are expanded into Laurent series,and then the coefficients of complex stress function are solved by power series method. The derived solution is applied to an example and a comparison is made using FEM method to show the accuracy of the methods,the results of this paper are almost the same as those of the FEM method,and the error is about 2%. The result shows:(1) The method presented in this paper is applicable to a shallow buried rectangular tunnel;(2) The complex function method proposed in this paper is characterized by clear steps,fast convergence and simple operation.