Abstract: Based on the inherent anisotropy and induced anisotropy of soil,transversely isotropic elastic constitutive relations are adopted to simulate elastic half-space of foundation.The relation between displacement and displacement function is proposed by extending Love displacement function to transversely isotropic elastic half-space. Then the general solutions of stress and displacement for non-axisymmetric problems are obtained by Hankel transformation. The axisymmetric elastic half-space solutions evolved from the general solution in this paper are in accordance with the classical ones.