A simplified model for cilia-induced flows in tubules is presented. Each cilium is a long slender body which is constrained to move similar to its beat. An array of cilia is defined and coordinated in such a way as to represent the metachronal wave. The velocity field is represented by a distribution of viscous fluid singularities (Stokes flow) along the centerline of each slender body. The total mean velocity field due to all the cilia is obtained. It is found that backflow (reflux) can occur near the walls for cilia exhibiting antiplectic metachronism. Maximum flow rates are obtained for cilia whose length is 0.3 to 0.6 the radius of the tube.