If it is assumed that the effect of radial flow can be neglected, then the vortices which are shed from the trailing edge of a propeller blade can be said to lie approximately on helical lines. These vortices form a vortex sheet which for practical purposes is assumed to extend unaltered downstream to infinity. If the propeller blade is approximated by a lifting-line of bound vorticity, then the velocities at the blade induced by the trailing vortex system can be derived from the simple flow conditions in the hypothetical far wake where the vortex sheets extend equally to infinity in both directions. Results are already well-known for the case where the vortex sheets exist in free space. It is the purpose here to examine the effect of adjacent boundaries, such as the hub and the duct wall of a ducted propeller. The results also relate to a test propeller in a tunnel.