This work concerns the flow of Jeffery and Newtonian fluids through a composite porous channel in the presence of a uniform magnetic field applied perpendicular to the direction of flow. The mathematical formulation of this problem represents the flow of Jeffery fluid through the porous channel sandwiched between two porous channels of the Newtonian fluid. The horizontal composite porous channel is divided into three porous channels of the same width and the fluid flow occurs due to a constant pressure gradient. The Jeffery equation has been used for the middle porous channel while the Brinkman equation has been employed for lower and upper porous channels. Continuity of velocities, continuity of stresses at interfaces, and impenetrability conditions at the outer surface of the composite porous channel have been used as boundary conditions. Analytical expressions for velocities, volumetric flow rate, and shear stresses are obtained for the respective channels. Effects of the viscosity ratio parameter (β), Hartmann number (<i>M</i>), Jeffery parameters (λ<sub>1</sub>), and permeability parameters (η) on the flow rate and fluid velocity are explained graphically and discussed. Numerical values of volumetric flow rate with respect to different flow parameters such as Hartmann number, viscosity ratio, and Jeffrey parameter are presented in tabular form.