A conducting half-space, permeated by an initial magnetic field governed by the generalized equations of thermoelasticity is considered. The bounding plane is acted upon by a combination of thermal and mechanical shock. The formulation is applied to both generalizations, Lord-Shulman theory and the Green-Lindsay theory, as well as to the coupled theory. Laplace transform techniques together with the method of potentials are used. The inversion of the Laplace is carried out using a numerical approach. Numerical results for the temperature, the stress and the induced magnetic and electric field distributions are obtained and illustrated graphically for a particular case. Comparisons are made with the results obtained in the case of the absence of the magnetic field.