With the development of urban construction in China, more and more applications of rectangular tunnel are emerging, but the theoretical research on rectangular tunnel is rarely seen. In this paper, the elastic theoretical calculation model of rectangular tunnel in semi-infinite space is established. The coefficients of conformal mapping function are determined by the least squares iterative method. The calculated region is mapped to a concentric ring on the complex plane. Then, the Muskhelishvili complex function method is used to expand the stress function in the calculated region into the form of Laurant series, and the zero stress boundary of the ground surface and the radial displacement boundary of the rectangular hole are given. The field of stress and displacement of the rectangular tunnel in semi-infinite space under the given displacement condition are obtained. The effects of different height-width ratios, Poisson’s ratio and depths on displacement and stress fields are analyzed, and the general rules of displacement and stress fields in rectangular tunnels are summarized. The results show that the settlement curve is no longer similar to a Gaussian curve with a smaller aspect ratio, a larger Poisson ratio and a smaller buried depth. The variation of these parameters will also affect the size and distribution of the stress field and displacement field to different degrees.