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[en] The present investigation deals with the mathematical modelling and analytical thinking to uncover the various facets of the propagation of Rayleigh waves in an Earth’s crustal layer. This work has been carried out when the wave is passing through a pre-stressed anisotropic layer of finite thickness, lying over a semi-infinite medium with void pores. The upper boundary plane of the crustal layer has been thought to be a free surface. Displacement components of the wave for both the media have been derived analytically. Appropriate boundary conditions have been well satisfied with the aid of displacement and stress factors in order to get the desired dispersion relation. A comparative study has been performed graphically taking anisotropic, orthotropic and isotropic strata, in order to show the impact of initial stress and thickness on the propagation characteristics of Rayleigh waves. The present work may establish a program to connect theoretical results with subject area applications.