The problem of peristaltic flow in a channel is solved using the incompressible and magnetohydrodynamic (MHD) Oldroyd-B fluid. The induced magnetic field effects are incorporated in the mathematical modeling. Computations are performed for the small wave number. The obtained mathematical results show that the induced magnetic field effects taken into account in the model substantially affect the flow quantities. It is found that relaxation and retardation times have opposite effects on the flow quantities such as velocity and pressure rise. Moreover, it is observed that induced magnetic field and current density are larger for Oldroyd-B fluid than for the viscous fluid. The salient features of the emerging flow parameters are examined by graphs.