The purpose of this book is to present a computer oriented numerical approach to study the blood flow in presence of transverse magnetic field. Here in all the problems, blood is assumed to be a Non Newtonian fluid. Mathematical formulation of the problem under consideration is presented and the similarity transformation is applied to reduce the system of partial differential equations and their boundary conditions describing the problem into a boundary value proem of ordinary differential equations. The equations are solved numerically by shooting techniques and the results are shown graphically.Emphasis has been given on the influence of magnetic parameters. From the study we can conclude that the magnetic field controls the velocity, flow rate and wall shear stress in human blood circulatory system. This book may help the researchers in this field. So for the benefit of the researchers the coding written in C language for the concerned boundary value problem is given at the end of each chapter.