Keeping in mind the applications of the flow through porous medium in geophysics, particularly in the study of earths core, importance of viscoelastic fluids in industry and chemical technology and presence of dust/suspended particles in fluids; the hydromagnetic stability of stratified Rivlin-Ericksen fluid saturating a porous medium in the presence of rotation is presented. The stability of the motionless horizontal layer of the fluid having vertical stratifications of the physical parameters; density, viscosity, viscoelasticity, medium porosity, medium permeability, particle number density and magnetic field is considered. After linearizing the relevant hydromagnetic equations, the perturbed quantities are analysed in terms of normal modes. Dispersion relation governing the effects of viscoelasticity, porosity, medium permeability, suspended particles, rotation and magnetic field on the stability of Rivlin-Ericksen fluid is derived. The system is found to be stable for the case of stable stratification as in the case of Newtonian fluids. For the case of unstable stratification, magnetic field succeeds in stabilizing the otherwise unstable system for certain wave number range. The behavior of growth rates with respect to Alfven velocity, medium permeability, suspended particles and angular velocity are found analytically as well as numerically. It has been found that the growth rate decreases with the increase in Alfven velocity and angular velocity; and it increases with the increase in medium permeability and suspended particles.

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