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In this paper, a theoretical investigation is described of the propagation behaviour of Love-type waves in a functionally graded material layered structure. The Wentzel–Kramers–Brillouin (WKB) method was applied to obtain the analytical solution for the functionally graded material layer. The study was carried out to investigate the transference of Love-type waves in a functionally graded material layer bounded by a viscous fluid layer and a highly anisotropic half-space. Two cases were studied, one in which the material property variation of the functionally graded material layer was arbitrary and one in which the material property variation was taken as exponential. A variable separation method was employed to obtain the displacement components in both the viscous liquid and the highly anisotropic medium. Profound effects of material gradient coefficient, viscous coefficient, liquid mass density, initial stress parameter and wavelength on real and imaginary components of phase velocities were established. Some numerical calculations were also made. The considered model facilitates a theoretical foundation and practical application for the development of surface acoustic wave devices. [ABSTRACT FROM AUTHOR]