This book contains study of boundary layer flow problems related to magneto hydrodynamic non- Newtonian fluid flows using quasilinearization technique. This study is essentially numerical in character, Constitutive equations are converted to ordinary differential equations and then Quasilinearization technique is applied to get numerical solution. In four of the problems studied, the fluid under consideration is of Walters Liquid B model. In one of the problems a power law fluid model is considered which has the facility of distinguishing the non-Newtonian fluid with the other cases. In all the problems the relevant flow field variables like velocity and temperature are numerically evaluated for diverse values of the fluid flow parameters that emerge in the problems. The solutions obtained for the problems in the thesis using the numerical approach stated are in good agreement with the corresponding numerical results obtained through analytical solutions. This strengthens the belief that for problems where in analytical solutions are eluding can be treated by the quasilinearization technique applied in the present book.