The study of visco-elastic fluid flows has gained significant attention in recent years due to its wide application in various branches of science and technology. The effects of magnetic field on the flow of an electrically conducting fluid play an important role because of its astrophysical, geophysical and engineering application. The flow through porous medium is quite prevalent in nature and has wide application in industrial, bio-physical and hydrological problem, particularly in petroleum, chemical and nuclear industries. Heat and mass transfer theory has practical importance for increasing the process rates in atomic power engineering, chemical engineering, space research and various branches of industry and agriculture. This study deals with the theoretical investigation of flow behaviour of visco-elastic fluid characterized by Walters liquid (Model B′) under different valid and suitable boundary conditions. The results reveal various aspects of the additional terms in the constitution equations as compared to Newtonian fluid.