The present paper explores a comparative study of two non-Newtonian mathematical models with porosity. The first mathematical model is based on the Power law model with porosity, and the second mathematical model is developed on the Maxwell principle having porosity. An attempt has been made to study how the shear-thinning viscoelastic affects the theology of blood under the magnetic field and porosity, when porosity through the vessel wall is taken into account with magnetic field in the blood arteries. The solution has been obtained by solving the differential equations occurring during the mathematical modeling by Finite Difference Method.