In this article, an estimation is made to investigate the transient phenomena in the magneto-thermoelastic model in the context of the Lord and Shulman theory in a perfectly conducting medium. A finite element method is proposed to analyze the problem and obtain numerical solutions for the displacement, temperature, and radial and hoop stresses. The boundary conditions for the mechanical and Maxwell’s stresses at the internal and outer surfaces are considered. An application of a hollow cylinder is investigated where the inner surface is traction free and subjected to thermal shock, while the outer surface is traction free and thermally isolated. The displacement, incremental temperature, and the stress components are obtained and then presented graphically. Finally, the effects of the presence and absence of reinforcement on the temperature, stress, and displacement are studied.