Abstract
We use the compact harmonic general solutions of transversely isotropic electro-magneto-thermo-elastic material to construct the three-dimensional Green's function for a steady point heat source acted in the interior of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material by five newly introduced harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results are given graphically by contours.