The transversely isotropic property of rock and soil layers can be shown in their deformation and strength properties because of the action of gravity. A numerical method and its corresponding Fortran codes were developed for assessing the additional stress and displacement fields in transversely isotropic foundation. The proposed method is based on the fundamental solutions for two joined transversely isotropic solids and integrates it over the distributed load by the use of a two-dimensional numerical integration after discretizing the loading area into a limited number of 8-noded isoparametric elements. The proposed method can be used for the analysis of half-space foundations with arbitrary loading areas and uniformly distributed loads, and very high computational accuracy can be obtained. Then with the use of the computer program, the influence of anisotropy was analyzed on the additional stress below the rectangular base due to a normal or tangential load case. Results show that the anisotropy of Poisson’s ratio has almost no effect on the additional stress. The anisotropy of elastic modulus exerts an obvious influence only under a normal load case. Except for the additional stress parallel to the isotropy below the corner point, the anisotropy of shear modulus all has an obvious influence.