Abstract: Based on the three-dimensional analytical solution derived from the fundamental equations, the generalized solutions of Cerruti’s half space problem are obtained using the displacement function method under the conditions that the characteristic roots are not equal. Hankel integration transform method and Bessel function theory are used. The generalized solutions of Cerruti’s half space problem degenerate into the classical isotropic Cerruti’s half space problem by correlative coefficient transformation. Distribution of displacement and stress in the transversely isotropic foundation are compared with those in the isotropic foundation．Distributed trend of the displacement field along the depth direction is nearly identical for two different models with given parameters, but there is remarkable difference for the stress field in two kinds of foundation.