In this research, we analyzed the effect of the magnetic field on the axial velocity function, as well as the stream function of non-Newtonian Wallers-B fluid in the inner duct and walls of curved peristaltic channels. This model was examined assuming along wave length and a low Reynolds number relative to a small Brinkman number (Br) using the modern and effective technique of the Mathematica program, the exact solutions of the governing partial differential  equations were found. After they were converted to ordinary differential equations. We verified the numerical results through the graphs of all the physical parameters and used the regular perturbation method to reach the numerical solutions for both the axial velocity and flow functions,  we conducted the discussion based on the graphs obtained in the Mathematica soft ware for the relevant parameters and it turned out that they are parabolas  where the velocity increases with the increasing  the parameters values for the curved walls and the behaviour here seems some what oscillatory with   increasing the curvature parameter .