Propagation of electro-magneto-thermoelastic disturbances produced by a thermal shock in a conducting elastic half-space investigated. The formulation applied to two-dimensional equations of the three-phase-lag model, Green–Naghdi theory without energy dissipation (G–N II) and Green–Naghdi theory with energy dissipation (G–N III). The normal mode analysis is used to obtain the analytical expressions of the considered variables. Comparisons are made with the results predicted by three theories in the absence and presence of a magnetic field as well as the two-temperature parameter. The results indicated that the effect of time, magnetic field, internal heat source, and two-temperature parameter are very pronounced.