A numerical method based on the finite element method is used for an investigation of viscous, incompressible fluid flowing in a channel with slowly varying cross-section with absorbing walls. The proposed mathematical model can be applied to understand the flow behaviour of a fluid in renal tubules. The method is not restricted by the parameters in the problem such as wave number, permeability parameter, amplitude ratio and Reynolds number. The effects of these parameters on the transverse velocity and mean pressure drop is studied and the results are presented graphically. Results show that the parameters cause a significant change on the flow.