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This work depends on the fluids which is classified in to two types i.e., Newtonian and Non-newtonian. These are related to Industrial, Technological and Bio-medical problems. The flow through porous medium is used in the fields of agricultural, chemical engineering, water resources etc. Porous medium defined as a solid which contains a number of small holes distributed though out the solid. The study of these run-up flows is gaining more importance due to its wide applications in different technologies. We extended this work by taking a second order Rivlin-Erickson fluids. The equations are solved by using Laplace Transformation Technique. The formulas are taken from so many governing equations which can be seen in the thesis. The solution of the problem is obtained from different Pressure gradients. At last we can observe so many variations by seeing graphs and tables.