Stability of a rotating film flow attached inside a circular cylinder was analyzed on a linear basis, where the cylinder is at rest and the basic flow is assumed to be kept rotating under the imposition of an artificial body force acting in the azimuthal direction. A traveling‐wave mode that is intrinsic for a film flow on a vertical or an inclined flat plate and a centrifugal instability mode are obtained as unstable modes. The effect of a superimposed shear flow in the axial direction was also examined and it was shown that the shear flow exerts a stabilizing effect on the centrifugal instability mode.