Although the theory of Giordmaine and Wang adequately predicts the centerline intensity of a molecular beam from a channel source, it is less successful in describing the angular distribution. This deficiency has been ascribed to a nonzero number density at the tube exit. The end conditions chosen by previous workers lead to angular distributions which fail to satisfy total flow and average cosine restrictions. A method of choosing the parameters of the linear density profile which satisfies these integral constraints is described. The computed angular distributions according to the theories utilizing different end conditions differ very little from each other, but represent a clear improvement over Giordmaine and Wang's angular distribution.