In this paper, the propagation of Rayleigh waves in a crystalline medium of finite thickness laid over an elastic half-space with sliding common interface is studied. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the elastic half-space is under the influence of gravity. The main aim of the paper is to establish the dispersion equation of the wave and investigate the effects of involved parameters on the phase velocity of the wave. Numerical examples for the crystalline medium, such as anisotropic Vosges sandstone, monoclinic coesite, orthotropic Rochelle salt and simply isotropic have been considered. Based on the obtained dispersion equation, effects of magneto-elastic coupling, hydrostatic stress and Biot's Gravity parameters on the phase velocity of Rayleigh wave in the different crystalline media are analysed and illustrated graphically. © 2018 Elsevier Ltd