In this paper, we have studied the joint effects of slip and aligned magnetic field on the peristaltic transport of a Williamson fluid in an elastic conduit with porous medium. The basic equations of Williamson fluid model in Cartesian coordinate system are built and simplified by using small Reynolds number and long wave length approximations. The simplified nonlinear equations are solved by adapting the perturbation method. The stream function and the axial velocity expressions are obtained. The impacts of important physical parameters on the flow are shown in graphs and discussed in detail. © 2021, Springer Nature Singapore Pte Ltd.