<p>A theoretical model is developed to study the radiation characteristics of screech tones and their harmonics for under-expanded supersonic jets in apping and helical modes. The model is constructed based on the distributed Gaussian pulse train sources. Compared with the existing models, the present model not only obtains the directivity patterns of the screech harmonics but also provides their relative amplitude hierarchy. Validation is performed using existing experimental and numerical datasets. The results show that the directivity of the harmonics, harmonic-specific phase distributions, and dominant radiation azimuthal ranges of different harmonics agree well with the established data. The inherent symmetric and antisymmetric phase formations associated with different harmonic modes are confirmed. Significantly, the analysis indicates that the intensity of the second harmonic can exceed that of other modes over a wide azimuthal range in the jet sideline direction, attributed to the superposition of the screech sources. Furthermore, the phase synchronization phenomenon at the nozzle exit is elucidated based on the model.</p>