A surface distribution of point forces has been used to calculate the Stokes flow drag on a thin flat ring moving either parallel to or perpendicular to the axis of rotational symmetry. The results for motion parallel to the axis are confirmed by experiment. The drag is found to depend primarily upon the outside diameter of the ring and to be relatively insensitive to the inside diameter, in contrast to measurements at high Reynolds number. When the inside diameter is zero, the results agree with the known exact solutions for the circular disk.