Abstract: With the aid of the basic theorems of Fourier transformation and Fourier series,the general solution of a pair of edge cracks at the interfaced of four different media in a rectangular sheet under longitudinal shear stress is found in this paper.It is of interest to note that the stress intensity factor of this problem is independent of the material constants of the composite rectangular sheet.The conclusion is no doubt of great importance to designers and experimenters because there is no need to carry out unnecessary tests.