In this paper, a linearly magneto-electro-elastic (MEE) multilayered half-space which is dynamically loaded over a finite patch located either on the surface or internally within any layer is addressed. The completely coupled system of equations of motion for MEE is applied. The unknown primary field quantities consisting of displacements, electrical potential and magnetic potential are expressed in a cylindrical system of vector functions, where each of the vector functions is written in terms of the product of Bessel functions and Fourier series. In so doing, the components of displacement vector and traction tensor in the physical domain are expanded in terms of a set of expansion coefficients in the Hankel–Fourier transformed domain. In each field point the calculated expansion coefficients in the transformed domain are utilized to calculate the unknowns in the physical domain by integration. Different sets of numerical analyses are presented to investigate the effects of material anisotropy, material coupling, loading frequency and stacking sequences of layers on the responses due to internal/external loadings.