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An analytical solution for a non‐circular tunnel excavated in an elastic homogeneous half‐plane is obtained, which considers gravity and different lateral pressure coefficients. The solution is deduced using the complex variable method, mapping the region containing a non‐circular tunnel onto a circular ring. The basic equations for the analytic functions are established using the stress boundary conditions at the ground surface and the edges of the tunnel and the analytical functions are solved by the power series method. In the process of solving, the Fourier series was used. To elaborate the solution process clearly and verify the correctness of the solution, a shallow quasi‐ellipse tunnel was analyzed as a computational example, and the results obtained using the presented analytical method are compared with that obtained by the numerical software ANSYS. [ABSTRACT FROM AUTHOR]