An analysis has been carried out to evaluate the sound radiation from a finite length unflanged, hard walled circular duct with uniform axial flow, both inside and outside the duct, using the Wiener–Hopf technique (in particular, Jones’ method). The theory developed includes many of the earlier results for the semi‐infinite length duct carried out by other authors, in particular, Lansing, Carrier, and Vajnstejn, in the appropriate limit. The acoustic model employed simulates the noise radiation from a turbojet aircraft engine, in flight, at low to medium specific thrust levels such as landing or steady cruise flight. It therefore includes the diffraction of sound at both duct ends and the mean convection of sound by the axial duct and external flow fields. However, the refraction effects due to nonuniform exterior flow fields which are encountered near the inlet and exhaust under conditions of high thrust (i.e., takeoff) are excluded. This study is presented in two parts. The first part deals with the theoretical development of the model utilizing the Wiener–Hopf techniques. The second part presents some computed radiation characteristics for typical duct configurations.