This paper considers the creeping flows generated by a disk moving edgewise parallel to a rigid wall or free surface, a disk oscillating edgewise in unbounded fluid and a hole in the rigid plane that bounds a shear flow excited by a parallel moving plane. The analyses for the three cases follow a similar pattern and several simplifying strategies are introduced to obtain significant improvements on the presentations suggested by previous work on such flows. Indeed, the resulting integral equations for the first disk problem are similar to those solved for the corresponding broadside motion. The drag force is shown to slowly approach its limit value as the disk is placed nearer to the free surface. The oscillatory hydrodynamic force is shown to have only Stokes and Basset components. The error in previously assuming the shear flow to extend to infinity is shown to be of orderH−3, whereHis the separation distance between the bounding planes.