The present study investigates the mathematical inspection of Stoneley wave propagation through the corrugated irregular common interface of two dissimilar Magneto-elastic Transversely Isotropic (MTI) half-space media under the impression of hydrostatic stresses. To enumerate the Lorentz's force besmeared in the structure, the generalized Ohm's law and Maxwell's equations were considered. The interior deformations were analytically calculated to obtain the wave frequency equation through the prescribed boundary conditions. To investigate the impacts of irregularity and various affecting parameters such as magnetic couplings and hydrostatic stresses on the wave propagation, frequency curves formed for the phase velocity of the wave. © 2021 Sharif University of Technology. All rights reserved.