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In this paper, shear waves propagation in a non-homogeneous anisotropic incompressible medium under influence of the electromagnetic field, gravity field, rotation and initially stressed medium has been studied. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, magnetic field, rotation, gravity field, non-homogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear waves has been obtained. The dispersion equations have been obtained and investigated for different cases. In fact, these equations are an agreement with the corresponding classical results when the medium is isotropic. The results obtained are discussed and presented graphically. The results indicate that the effects of gravity field, initial stress, magnetic field, electric field, non-homogeneous, anisotropy and rotation are very pronounced.

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