An analytic method originated by Y. H. Chin was extended to calculate the electromagnetic fields and the longitudinal impedance due to coherent wiggler radiation (CWR) in a rectangular chamber. The method used dyadic Green functions based on eigenfunction expansion method in electromagnetic theory and was rigorous for the case of straight chamber. We re-derived the theory and did find the full expressions for the longitudinal impedance of a wiggler with finite length. With shielding of chamber, the CWR impedance indicated resonant properties which were not seen in the theory for CWR in free space. Show Partial Abstract