This work is concerned with the study of vibrations induced by a laser beam in the context of different theories of magneto thermoelasticity, coupled thermoelasticity (CTE), thermoelasticity with one relaxation time (L-S) and thermoelasticity without energy dissipation (G-L), of an infinitely long solid conducting circular cylinder. The surface of the cylinder is assumed to be traction free. The temporal profile of the laser beam is considered as non-Gaussian. The cylinder is considered to be made of an isotropic homogeneous thermoelastic material put in a uniform magnetic field in the direction of the axis. This produces an induced magnetic field and an induced electric field. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. The temperature, displacement, stresses, induced magnetic field and induced electric field are calculated numerically then represent the result by graphs.