Active systems are those where energy is constantly injected by an external source. A typical example is the cytoskeleton of cells made of actin filaments and myosin molecular motors which consume ATP. In this paper, we study the behavior of an active polar gel in a thin, non-uniform channel modeled as a two-dimensional strip with periodically undulated walls. Using our recent hydrodynamic theory of active polar gels, we show that the orientation of the actin filaments parallel to the walls of the channel induces a flow even in the absence of any pressure gradient. The average flow is a simple shear if there is a phase difference between the undulations of the two walls of the channel. We also discuss applications of these results to various biological problems.