Abstract: The presence of inclusions plays an important role in the fracture behavior of engineering material, especially for composite materials. From the viewpoint of inhomogeneity in solids, if the value of the elastic modulus is much greater that of the matrix is, it appears reasonable to consider it as a rigid line, which causes serious stress concentration. In this paper, longitudinal shear problem of the double rigid lines is dealt with. By using the conformal mapping of elliptical function and the symmetric principle of Riemann-Schwarz, we present the solution in closed form. From the limited case of the present solution, some existing results can be obtained.