The linear hydrodynamic stability of the flow through an annulus composed of two concentric porous circular cylinders with the outer cylinder moving is examined. Axisymmetric disturbances of the flow, which is produced by a longitudinal pressure gradient, a cross-flow and boundary motion, are examined using numerical methods producing neutral stability curves which show that the flow is stabilized by boundary motion even in the presence of a destabilizing crossflow. Two special cases, annular Couette flow and transverse flow through an annulus, are also investigated and are found to be stable for small disturbances.