Using the double integral Fourier transformation, we construct solutions of space problems of the theory of elasticity and thermoelasticity for a half space with a locally distributed moving mechanical and thermal load on the surface. The obtained formulas allow one to find displacements and stresses in a half space for a velocity of the load smaller than the velocity of the Rayleigh wave. In the limiting case of the action of a fixed load, the obtained solutions coincide with known ones.