The phenomenon of transport of viscoelastic material in human body is a hot topic of research in biomechanical engineering. This topic has stimulated the attention of engineering scientists, modelers, numerical simulants and mathematical biologists. Biorheological flows are now experimentally exemplified by blood, bile, mucus, digestive fluids, synovial lubricants etc. On the other hand the peristaltic pumping of fluid transport is due to a wave contraction/expansion traveling along the length of a distensible channel/tube containing liquids. This mechanism generally appears from a region of lower to higher pressure. Many muscles possess such inherent characteristics. Specific examples for physiological processes may include eggs motion in the female fallopian tube, spermatozoa transportation, transport of bile in duct, intrauterine liquid transportation in the uterine cavity, blood circulation in small vessels, gall bladder with stones, locomotion of animals like larvae of certain insects and earthworms, urine passage from kidney to bladder, transport of embryo in non-pregnant uterus etc. Many biomedical systems for instance dialysis machine, blood pumps machine, heart lung machine and roller and finger pumps operate under peristalsis in order to cater the specific day to day requirements. Such activity is also quite prevalent in industrial technologies for example chamber fuel control, micro-pumps in pharmacology and toxic waste conveyance in chemical engineering. Continuous efforts for refinements in designs sure acquire much complex models of peristalsis through non-Newtonian materials. Motivated by this fact, the primary motto here is to model and analyze the peristaltic motion of non-Newtonian materials in a channel. Further the magnetomaterial aspect in such consideration has relevance with blood dynamics, blood pump machines and magnetohydrodynamic (MHD) peristaltic compressor. Blood flow rate is greatly affected under magnetic field.With this motivation, this thesis is organized as follows. First chapter provides literature review. Second chapter contains some standard definitions and flow equations. Dimensionless numbers and expressions for Jeffrey fluid are included.Third chapter examines Peristaltic flow of viscous liquid in curved tube. Fluid is electrically conducting. Relevant problem is modeled. Lubrication approach is followed for the equations in tractable form. Resulting problem is solved for asymptotic analytic solution. Axial velocity, pressure gradient and pressure rise per wavelength are analyzed in detail. Comparison with existing studies is presented. Major findings are given in conclusions. Material of this chapter is published in “Results in Physics 7 (2017) 3307-3314”, [1]. Chapter four introduces existence of Hartman boundary layer for peristaltic flow in curved tube. Equations for Jeffrey liquid in curved tube are modeled. Applied magnetic field is taken large. Both quantitative and qualitative approaches are utilized. Examination of Hartman layer is made by considering two term analytic solution using matched asymptotic technique. Traditional analysis of obtaining analytic results is extended for dynamical system of problem in order to understand the flow behavior. Nonlinear autonomous differential equations are established. These equations characterize path of fluid particles. Equilibrium plots give a complete description of various flow patterns developed for complete range of flow variable in contrast to existing reported studies which describes flow patterns at some particular value of parameter. Bifurcation diagrams are displayed. The observations of this chapter are published in “Communications in Nonlinear Science and Numerical Simulation”, [2]. Chapter five is prepared for flow of dusty liquid bounded by a stretching sheet. Constant strength of applied magnetic field is chosen. Exact analytic solution to derived problem is constructed.A comparative study with existing numerical solution is made. Skin friction and velocity results are given. Physical interpretation to influential variables in obtained solutions is assigned. Findings of this chapter are published in “Mathematical Problems in Engineering 2307469 (2017)5, [3].