Analytical results are reported on magneto‐thermoelastic coupled wave propagation in a solid medium. The relevant frequency equations have been obtained by solving equations of elasticity, taking into account the effects of thermal field, magnetic field and the electromagnetic equations of Maxwell. The nature of frequency has been discussed in different cases. It is also shown that, if the frequency is sufficiently smaller than a certain critical frequency, the attenuation factor as well as the phase velocity retain the same characteristics as in a purely thermoelastic body, provided the thermoelastic coupling factor is suitably increased.