Abstract: A general three-dimensional solution for transversely isotropic foundation in the image field was strictly obtained by use of the displacement function method.The Galerkin’s displacement function for isotropic elasticity was modified,and Hankel integration transform and Bessel function theory were employed in the solution.With the Hankel integration inversion shift theory,the fundamental expression of strain and stress in the transversely isotropic foundation was presented for different cases that the characteristic roots were equal or not.The solution included the axisymmetric problem and asymmetrical problem.The obtained general solution could be simplified to the general solution of axisymmetric problems of a transversely isotropic foundation through the coefficient transform.It could be used to solve some specific asymmetrical problems for semi-infinite space under different boundary conditions.