In this paper, the Mindlin's solution of plane strain and axis-symmetrical problems within an n-layer elastic system is obtained by the integral transform technique and the recurrence laws of matrices. Using this solution as the fundamental solution, a simple method was" established to calculate displacements in any internal point within multi-layered elastic medium by the somigliana formula. By this method, the progrmming is easy, while the accuracy and the speed of computation are high.