Abstract: This paper establishes two kinds of boundary conditions and two corresponding displacement functions for analysing the heterogeneous, transversely isotropic layered and elastic half-space subject to body force, and concentrated and/or distributed loads on horizontal planes. Directions of such forces and loads may be arbitrary, and finite layer analysis has beed used for computing quite a number of such problems, giving results in good agreement with elassic solutions due to Boussinesq, Cerrti, Mindlin and others.The method presented in this paper can be handled with small and medium-size computers.