The characteristics of fluid flow through three porous layers are investigated. The two outer porous layers are considered to be of infinite width, while the middle porous layer is assumed to be of finite width. The mathematical model of the fluid flow in the middle region can be described as laminar fully developed flow and is assumed to be governed by Brinkman equations. The flow through the upper and lower porous media is governed by Forchheimer equations. At the two interface regions between the middle finite width porous layer and the outer infinite porous layers, the continuity of the velocity and of the shear stress are imposed. Under these matching conditions, the exact solutions for the set of equations describing the flow velocity are obtained. It is found that the flow velocity is affected by two parameters, namely, Reynolds number and Darcy’s number. The effects of these parameters on the flow velocity profiles through the flow regions are investigated and presented.