Abstract <p>Sandwich structures with thin, stiff and heavy facings compared to the core are employed in civil and aerospace engineering, while those with thick, soft and lighter facings are preferred in precipitator plate applications. Insights gained into the behavior of horizontally polarized shear (SH) waves in sandwich structures can guide the design of more resilient and efficient composites, enhancing their performance under dynamic loading conditions. The dynamic behavior of a sandwich structure with symmetric facings is rigorously analyzed within the framework of the consistent couple stress model of elasticity. Harmonic wave solutions are derived, provided that they satisfy either traction-free or fixed boundary conditions on the faces, while maintaining continuity of tractions and displacements at the interfaces between the core and facings. This analysis uses the size-dependent consistent couple stress elasticity, which incorporates a length parameter (characteristic length) assumed to be of the same order as the internal microstructures of the material. Dispersion relations for the propagation of SH waves are calculated under both stress-free and fixed boundary conditions. Detailed mathematical results are provided, accompanied by graphical illustrations that show the impacts of characteristic length parameters and thicknesses of the core and facings on the phase velocity under both symmetrical and skew-symmetrical conditions.</p>