Integral expressions are derived for the displacement response tensor of a semi-infinite anisotropic elastic continuum of unrestricted symmetry to a concentrated force suddenly applied to its surface. The surface response is reduced to a one-dimensional integral for numerical evaluation, while the interior response is left as a two-dimensional integral. Calculated surface response functions for Cu(001) are presented. These display multiple Rayleigh wave arrival singularities as well as bulk wave arrivals. Calculated interior response functions for Zn(0001) are presented. These display bulk and head wave arrivals. In followup papers these methods will be used in the interpretation of capillary fracture generated waveforms measured in a number of different materials.