The aim of this investigation is to estimate the theory of generalized magneto-thermoelasticity to solve the problems of two-dimensional (2D) half-space under thermal shock, initial stress, and two temperatures. The governing equations are solved by using Lame's potentials method in the context of classical dynamical (CD) and Lord-Şhulman (LS) theories. The boundary conditions are as follows (i) the total normal stresses in the boundary equivalent to the initial stress; (ii) the shear stresses are vanished at the boundary; and (iii) the incidence boundary is thermal insulated. The reflection coefficients have been obtained for two incident *p*- and SV-waves. The results obtained for the incident waves calculated numerically by using appropriate metal and presented graphically. Comparisons have been made with the results obtained from the presence and absence of magnetic field and initial stress.