Morse's equation for the radiation impedance of a vibrating rigid piston is extended to give the generalized radiation impedancesZmnlof all modes in circular and annular ducts which have arbitrary wall admittance β and which terminate in an infinite baffle. The equation forZmnlis reduced to a single infinite integral which is a function of the mode radiation directivity factors. An infinite matrix equation is derived which relates the generalized mode reflection coefficientsRmnlto the radiation impedances. Results are presented which show that the duct‐wall admittance is a significant parameter in the effect of duct‐termination reflections and that mode‐coupling reflection effects may be more important than direct‐mode reflection effects.