We consider a system consisting of n elastic layers made of different transversely isotropic materials bonded to each other and the last layer bonded to an elastic half‐space made of a different transversely isotropic material. An arbitrary tangential displacement is prescribed over a domain S of the first layer, while the rest of the layer’s surface is stress free. The tangential contact problem consists of finding the complete stress and displacement fields in this system. The Generalized Images method developed by the author is used to get an elementary solution to the problem. We first consider the case of two layers and then generalize it for the case of n layers. The same problem is solved by the integral transform method, and it is shown that an integral transform can be interpreted as a sum of generalized images. The results are valid for the case of isotropy as well.
