Abstract <p>A mathematical model of dynamic processes in a bimorph plate composed of inhomogeneous pre-stressed piezoelectric and piezomagnetic layers is proposed. The model is based, on one hand, on the use of linearized constitutive relations and equations of motion for a pre-stressed magneto-electro-elastic (MEE) medium. On the other hand, it utilizes a numerical-analytical approach for solving dynamic problems for inhomogeneous pre-stressed MEE media. This approach involves reducing the boundary value problem formulated with partial differential equations to a system of initial-boundary Cauchy problems for the components of the extended stress tensor and displacement vector, combined with the application of efficient high-precision numerical solution schemes. The inhomogeneous piezoelectric and piezomagnetic layers of the plate are assumed to be made of functionally graded materials. A two-component model was used to simulate the inhomogeneity, wherein the parameters of the layer’s base material vary through the thickness until they match the parameters of the inclusion material. The initial strain state (ISS) within the plate’s constituents is homogeneous and is induced by initial mechanical stresses. Within the framework of the model and under the quasi-static approximation, the features of shear horizontal (SH) wave propagation in a plate made of pre-stressed functionally graded materials based on PZT-5H and CoFe₂O₄ are investigated. Wave propagation is initiated by a remote source of harmonic oscillations, assumed to be in a steady state. Perfectly bonded conditions are satisfied at the interface between the layers; the external surfaces are free from mechanical loads, electrically shorted, and magnetically open. The specific influences of the type and magnitude of the initial deformations in each layer on SH-wave velocities for different localizations of the plate’s inhomogeneity are investigated. The frequency ranges of the maximum and minimum influence of the layers ISS on the velocities of various SAW modes over a wide frequency range are determined. It is shown that in the case of an ISS with equal deformations in the layers, the influence of each layer’s ISS complements and reinforces the other. For the case of an ISS with different patterns of deformation in the layers, frequency ranges with partial compensation of the influence of each individual layer’s ISS are identified. The obtained results are presented in dimensionless parameters and may be of particular interest for the development, design, and optimization of new materials used in modern devices and instruments based on SH-SAWs.</p>