In this article, Maxwell’s viscous fluid movement is studied through a cylindrical symmetric tube (pore) with a complaint wall and this movement is peristaltic. The fluid’s compressibility and slip effect have been taken into consideration. The problem was solved with the perturbation approach in terms of small amount that triggers amplitude ratio. Second-order approximation, the net flux caused by the moving wave is determined for various physical parameters like the wall tension, damping force, wall rigidity, slip parameter, wave number, relaxation time and compressibility parameter. The impacts of interested parameters are discussed numerically and illustrated graphically. In various fields of study, such as biological sciences, There are many applications of this study represented in studying blood flow in living things and in industry as well as simulating fluid flow through flexible tubes.