In 1954, Gregorig formulated a theory for surface tension drained condensation on vertical ‘fluted’ surfaces, which have a special convex fin profile. Typically, such fluted surfaces must also have a drainage channel, in which the condensate generated on the special convex profile is drained by gravity force. The literature has been devoid of a satisfactory model to predict the condensation rate in the drainage channel. This paper formulates a theoretical method to predict the condensation rate in a drainage channel of rectangular cross-section. The model was used to predict the experimental data of Kedzierski and Webb, and is shown to provide an excellent prediction of the data. The prediction shows that the condensation rate in the drainage channel accounted for 6–32% of the total condensation rate on the Gregorig convex fin profile, as tested by Kedzierski and Webb. With slight modification, the drainage channel model may be extended to predict the condensation rate in drainage channels having other than a rectangular shape, e.g. a cosine shape.