Numerically investigated analysis occupying considerations free from long wavelength and creeping flow regime has been addressed in this paper for non-Newtonian Casson fluid induced by peristaltic activity. Rheological measurements have been exposed by fluid progression in the asymmetric conduit influenced by a normally settled magnetic field. The analysis is made without implementation of the lubrication theory which allows the role of inertial forces in the flow model not addresses before. Galerkin formulated finite element method is practiced by simplifying full Navier-Stokes equations to assure the appearance of non-trivial Reynolds number and wave independence in an ongoing study. The solution hinged based on code formulated in MATLAB for velocity distribution, pressure profiles, vorticity lines, and stream function is graphically plotted. It has been deduced that inflating the Casson fluid parameter (0.1≤β≤0.5) drives an inappreciable reduction in velocity close to the central region and vorticity lines to remain unaffected. An appreciable increase in bolus formation is inspected by rising time mean flow (1.1≤Q≤1.6) with the diffusion of streamlines in the provision of a progressive phase in waves.