Here an attempt has been made to investigate the magnetohydrodynamic (MHD) flow of a non-Newtonian fluid filling the porous space in a channel with compliant walls. Constitutive equations of a Jeffery fluid are used in the mathematical modeling. The flow is created due to sinusoidal traveling waves on the channel walls. The resulting problem is solved analytically and series solution for a stream function is derived. The effects of pertinent flow parameters are discussed through graphs.