The aim of the present numerical investigation is to explore the impact of magnetic field on peristaltic flow of an incompressible tangent-hyperbolic fluid in an asymmetric channel. The present physical model is developed based on the considered flow configuration and with the help of small Reynolds number approximations. The current flow problem is revealed under the influence of applied magnetic field. The asymmetric channel has been considered to narrate the present physical problem. Considered physical situation in the current investigation gives the unsteady coupled highly nonlinear system of partial differential equations. Also, the simplified equations for pressure, pressure gradient, and streamlines have been obtained with the help of suitable transformations. A regular perturbation scheme is employed to produce the semi-analytical results of the present problem. The influence of various physical parameters on pressure, pressure gradient, and streamlines are illustrated with the help of graphs. From the present analysis, it is observed that the increasing magnetic number decreases the pressure and pressure gradient in the channel. Also, the size of trapping bolus increases with increasing values of Weissenberg number. K E Y W O R D S asymmetric channel, magnetic field, peristaltic flow, Reynolds number 1 | INTRODUCTION Peristaltic flow of physiological fluids is a type of wave-frame movement existing inside the tube-shaped structures, which induces the motion of a particle/medium. Peristaltic transport mechanism is very important in many industrial and real-life applications. For instance, blood flow in the heart, lungs and dialysis works on the principles of peristaltic process. Also, other mechanisms include the peristaltic flow examples, such as movement of urine to bladder through kidney, motion of chyme in intestinal path, spermatozoa motion, movement of food in esophagus, vasomotion of arterioles, capillaries, and venules, and many other biomedical applications. However, in realistic view, the process such as sanitary fluid movement, corrosive fluids transfer, motion of toxic fluids in various industries, plasma flow, blood flow, alloys and liquid metals flow, heavy oil lubrication with greases, and many others will fail to follow the Newtonian flow conditions. However, for these types of practical applications, it is quite obvious to choose the non-Newtonian fluid flow behavior to determine the transport properties. Further, various researchers have considered and studied the different non-Newtonian fluids based on their practical applications and flow complexity. The theoretical and experimental study of peristaltic fluid flow in a pump was studied by Latham. 1 It is clearly observed from Latham's study that the variations in the velocity profile were useful to describe how viscosity causes the peristaltic pump to work. Also, forward and backward flow occurs even though there is no pressure across the pump. Further, Latham's study was continued by Jaffrin and Shapiro 2 and they described the influ...