The model of the equations of generalized magneto-thermoelasticity in an isotropic elastic medium with an initial stress is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under three theories of generalized thermoelasticity: Lord-Schulman with one relaxation time, Green-Lindsay with two relaxation times, as well as the coupled theory. The normal mode analysis is used to obtain the exact expressions for the considered variables. Some particular cases are also discussed in the context of the problem. Numerical results for the considered variables are obtained and illustrated graphically. Comparisons are also made with the results predicted by different theories (CD, L-S, G-L) in the absence and presence of a magnetic field, as well as initial stress.