In this study, the nonsymmetrical two dimensional elasticity problem of an elastic layer which is supported by two elastic quarter planes has been carried out. It is assumed that the contact between the layer and the supports is frictionless and only compressive tractions can be transmitted along the contact area. The problem is handled by using integral transform and singular integral equations techniques, and a computer program has been developed for solving the problem. Some numerical examples have been solved and the pertinent results were compared with those found by two other methods. The three methods, namely, the integral transform technique jointly used with a numerical solution technique for singular integral equations, the finite element method, and the boundary element method, being dependent on completely different mathematical concepts, show a very close match among their results and is a perfect sign of their reliability.