In a previous paper [1], we have obtained a general solution of three dimensional problem of the theory of elasticity for a transversely isotropic body. This general solution is applied in the present paper to the problem of equilibrium of a transversely isotropic half space. The following six problems are treated: 1) half space under given surface load, 2) half space under given surface displacement, 3) half space under given normal surface load and tangential surface displacement, 4) half space under given tangential surface load and normal surface displacement, 5) the contact problem of a rigid stamp upon a half space, 6) the problem of bending of thin plate resting upon a half space. It is found that, if, in problems 5) and 6), fricdonal force between stamp or plate and half space may be neglected, there exist simple relations between solutions for a transversely isotropic half space and corresponding solutions for an isotropic half space.