Impact of radially varying applied magnetic field on the peristaltic transport of a Carreau-Yasuda (CY) fluid through a curved channel is examined. Analysis is performed when the no-slip condition does not hold. Long wavelength and low Reynolds number approximations are taken into consideration in the mathematical formulation of the problem. Both differential equation and boundary condition are nonlinear. Resulting nonlinear equation subject to the nonlinear boundary conditions are numerically solved with Runge-Kutta fourth order with numerical Shooting. Impacts of sundry parameters on the quantities of interest are analyzed through plots. Results show that plots of the axial velocity are not symmetric about the center line for flow through curved conduits. Consequently the fluid flowing through a curved channel exerts additional stress on the inner wall of the curved channel. Such symmetry is restored when we move from curved to straight channel. Maximum fluid velocity decreases with an increase in the strength of applied magnetic field and the velocity slip parameter. Further the stress at the inner wall reduces by increasing the value of curvature parameter. (C) 2015 Elsevier Ltd. All rights reserved.