<p>This study examines the transmission of shear horizontal waves in a multilayered structure composed of direction-dependent magnetoelastic materials subjected to initial stress. The formulation incorporates both anisotropy and magnetoelastic coupling and exact analytical solutions are derived for wave transmission across layers. Variations in material combinations, anisotropy strength, magnetoelastic coupling and pre-stress are systematically analyzed to study their effects on the non-dimensional phase velocity and wave number. The novelty of this work lies in modeling the multilayered magnetoelastic medium to mimic Earth’s internal sublayers, where variations in density, inhomogeneity and mechanical properties significantly affect wave dynamics. This approach reveals unique transmission traits that conventional isotropic or homogeneous models cannot capture. The findings provide deeper insights into shear horizontal wave propagation with direct applications in geophysical exploration of Earth’s layered structure, nondestructive evaluation of composite materials and the development of magnetoelastic sensors and devices. Results are illustrated through graphs generated using Mathematica.</p>