This article investigates the peristaltic laminar flow of a two layered model in a channel containing Newtonian fluid in the core region and the region adjacent to the wall is filled with porous medium under the action of an external magnetic field by taking approximations of low Reynolds number and long wavelength. As a part of solution, the shape of interface for the fluid and porous regions were found independently. At the interface of the fluid, shear-stress jump boundary condition was applied. In peristaltic transport, the importance of physical quantities like pumping, axial velocity, and interface are discussed for different considerations of interest governing the flow like effective viscosity, Darcy number, permeability, stress jump constant, and Hartmann number, etc. It is noticed that increasing magnetic parameter results in enhancing the pumping of the fluid. Increasing magnetic field parameter, the axial velocity of the fluid reduces. That is, increasing magnetic parameter strengthens the magnetic field which applies a transverse force on fluid; hence, fluid velocity decreases. The significant observation is that, when stress jump constant β takes the values between 0 to 1 the axial velocity decreases gradually, and for β > 1 we observed no variation in axial velocity. Further, with an increase in shear-stress constant, the pressure rise enhances in pumping region. A sound knowledge on pumping of the fluid and shape of the interface may be useful to understand the gastrointestinal tract mechanism. © 2021 by Begell House, Inc.