This research is mainly concerned with studying the performance of the peristaltic flow of magnetohydrodynamic (MHD) viscous compressible flow under the impact of slip conditions, magnetic flux density, elastic features of the wave, and the liquid compressibility. The model taken represents a two-dimensional flexible sinusoidal rectangular duct with spring-damper backing. The perturbation approach is expanded as a series over the governing equations and the non-linear solution is introduced. Analytical relations describing the mean axial velocity, the mean velocity perturbation function, the net volumetric flow rate, the velocity corresponding to the elastic walls, and the critical wall tension are obtained with a small perturbation parameter known as amplitude ratio. The reversal flow occurs near the core of the channel when the critical tension is reached. The compliant wall features, magnetic flux density and slip conditions are strongly changing the dynamic behavior of the induced flow. The flow of biofluids through the human body is a good application related to this study.