This paper derives, for the first time, the complete set of three-dimensional Green’s functions (displacements, stresses, and derivatives of displacements and stresses with respect to the source point), or the generalized Mindlin solutions, in an anisotropic half-space $z>0$ with general boundary conditions on the flat surface $z=0.$ Applying the Mindlin’s superposition method, the half-space Green’s function is obtained as a sum of the generalized Kelvin solution (Green’s function in an anisotropic infinite space) and a Mindlin’s complementary solution. While the generalized Kelvin solution is in an explicit form, the Mindlin’s complementary part is expressed in terms of a simple line-integral over [0,π]. By introducing a new matrix **K**, which is a suitable combination of the eigenmatrices **A** and **B**, Green’s functions corresponding to different boundary conditions are concisely expressed in a unified form, including the existing traction-free and rigid boundaries as special cases. The corresponding generalized Boussinesq solutions are investigated in details. In particular, it is proved that under the general boundary conditions studied in this paper, the generalized Boussinesq solution is still well-defined. A physical explanation for this solution is also offered in terms of the equivalent concept of the Green’s functions due to a point force and an infinitesimal dislocation loop. Finally, a new numerical example for the Green’s functions in an orthotropic half-space with different boundary conditions is presented to illustrate the effect of different boundary conditions, as well as material anisotropy, on the half-space Green’s functions.

*Elasticity*, Kluwer Academic Publishers, Dordrecht, The Netherlands.

*Anisotropic Elasticity*, Oxford University Press, Oxford, UK.

*Elasticity and Geomechanics*, Cambridge University Press, Cambridge, MA.

*Micromechanics of Defects in Solids*, 2nd Ed., Martinus Nijhof, Dordrecht, The Netherlands.

*Contact Problems in the Classical Theory of Elasticity*, Sithoff and Noordhoff, The Netherlands.

*Applications of Potential Theory in Mechanics: A Selection of New Results*, Kluwer Academic Publishers, Dordrecht, The Netherlands.

*Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering*, Kluwer Academic Publishers, Dordrecht, The Netherlands.

*Soil Mechanics*, 5th Ed., Chapman & Hall, New York.

*Theory of Plates and Shells*, 2nd Ed., McGraw-Hill, New York.

*Proc. 4th Pacific International Conference on Aerospace Science and Technology*,” pp. 1–7.

*A Treatise on the Mathematical Theory of Elasticity*, 4th Ed., Dover Publication, New York.

*Mathematical Theory of Elasticity*, McGraw-Hill, New York.

*Theory of Dislocations*, 2nd Ed., John Wiley and Sons, New York.