Two different non_Newtonian models for blood flow are considered,first a simple power law model displaying shear thinning viscosity,and second a generalized Maxwell model displaying both shear thinning viscosity and oscillating flow viscous_elasticity.These models are used along with a Newtonian model to study sinusoidal flow of blood in rigid and elastic straight arteries in the presence of magnetic field.The elasticity of blood does not appear to influence its flow behavior under physiological conditions in the large arteries,purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions.On using the power law model with high shear rate for sinusoidal flow simulation in elastic arteries,the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to Newtonian fluid for the same pressure gradient.The governing equations have been solved by Crank_Niclson scheme.The results are interpreted in the context of blood in the elastic arteries keeping the magnetic effects in view.For physiological flow simulation in the aorta,an increase in mean wall shear stress,but a reduction in peak wall shear stress were observed for power law model compared to a Newtonian fluid model for matched flow rate wave form.Blood flow in the presence of transverse magnetic field in an elastic artery is investigated and the influence of factors such as morphology and surface irregularity is evaluated. Two different non_Newtonian models for blood flow are considered, first a simple power law model displaying shear thinning viscosity, and second a generalized Maxwell model displaying both shear thinning viscosity and oscillating flow viscous_elasticity.These models are used along with a Newtonian model to study sinusoidal flow of blood in rigid and elastic straight arteries in the presence of magnetic field. C elasticity of blood does not appear to influence its flow behavior under the physiological conditions in the large arteries, purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions.On using the power law model with high shear rate for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid to to Newtonian fluid for the same pressure gradient. equations have been solved by Crank_Niclson scheme.The results are interpreted in the context of blood in the elastic arteries keeping the magnetic effects in view. For physiological flow simulation in the aorta, an increase in mean wall shear stress, but a reduction in peak wall shear stress were observed for power law model compared to a Newtonian fluid model for matched flow rate wave form. blood flow in the presence of transverse magnetic field in an elastic artery is investigated and the influence of factors such as morphology and surface irregularity is evaluated.