This article concerns the investigation of the stress, temperature, and magnetic field in a transversely isotropic, elastic cylinder of infinite length and perfectly conducting material placed in a primary constant magnetic field when the curved surface of the cylinder is subjected to periodic loading. The analysis encompasses Lord and Shulman and Green and Lindsay theories of generalized thermoelasticity to account for the finite velocity of heat equation. The analysis of the numerical results for stress, temperature, and numerical values of the perturbed magnetic field in the free space is carried out at various points of the cylindrical medium. It is found that the effect of the applied magnetic field is an increase in the elastic wave velocity or, in other words, the increase of the solidity of the body. Furthermore, it has been shown graphically that the stress and perturbed magnetic field are modified due to the thermal relaxation …