The present study is concerned with the flow of a Newtonian fluid through a composite rectangular porous channel
sandwiched between micropolar and couple stress fluids. The horizontal composite porous channel is divided into three
porous channels of uniform width, and flow is induced due to a constant pressure gradient. The Brinkman equation is
used for the fluid motion in middle porous channel, while governing equations of micropolar and couple stress fluids
are used to describe the motion within the lower and upper porous channels, respectively. Expressions of linear velocity, microrotations, stresses (shear and couple) and flow rate are obtained analytically. Continuity of velocity, continuity of tangential stresses, no slip, no spin, and no couple stress conditions are used at interfaces and outer surfaces of the channel. Effects of permeability parameters, micropolar parameter, and pressure gradient on the flow rate and fluid velocity are discussed and presented graphically. Numerical values of flow rate (<i>Q</i>) for permeability, micropolar parameter, and pressure gradient are calculated and presented in tabular forms. MSC (2020): 76A05; 76S05; 76D05; 35C05.