This paper studies the effect of the magnetic field on a two-dimensional thermoelastic medium based on the Lord–Shulman theory of the body, which has a doubly porous structure. The normal mode analysis is used to obtain the analytic expressions of the physical quantities that we consider the solution form in the exponential image. In addition, a homogeneous double porosity thermoelastic half-space with the effect of the Lorentz force has been discussed. Besides, the equations of the generalized double porosity structure thermoelastic material with one relaxation time have been developed. The general solutions of the problem were found, under certain conditions. Moreover, the numerical results are discussed graphically in comparisons with the presence and absence of the magnetic field for copper material.