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In this manuscript, the propagation of strong shock wave in a non-ideal gas in the presence of azimuthal magnetic field with rotational effect is examined by using the Lie group of invariance technique with an assumption of uniform density in the undisturbed medium, whereas the azimuthal component of the fluid velocity and magnetic field are supposed to vary. The main advantage of this method is to reduce the number of independent variables by one. We obtained a special class of self-similar solutions to the problem, and the flow profiles are depicted graphically behind the shock followed by a brief discussion on the behavior of solutions through graphs. The effects of variation in non-ideal parameter, adiabatic index of the gas, Alfven-Mach number and ambient azimuthal velocity exponent on the flow variables are presented. All numerical calculations have been done using the "Mathematica"software.

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