Abstract: The propagation characteristic of horizontally polarized shear waves (SH-waves) in a periodic multilayered piezoelectric-piezomagnetic composite with initial stress was considered, where the propagation direction of SH waves is normal to the interfaces. The general solutions to the governing differential equations for piezoelectric and piezomagnetic layers are first derived. By applying the interfacial and periodic conditions to the general solutions, the explicit dispersion equation is obtained. For the periodically layered structure consisting of BaTiO3 layers and Terfenol-D layers, the dispersion equation is solved numerically to show the influence of the initial stress on the stop band effect and propagation velocity. The results obtained are useful for applications of layered piezoelectric-piezomagnetic composites to acoustic wave and microwave devices.