A mathematical model of steady, fully developed laminar flow in curved ducts is developed and used to derive a simplified computation method to be applied in another mathematical model predicting the flow in river bends. The laminar flow model is verified by comparing its results with analytical, numerical and experimental results reported in the literature. A series of shallow channel computations is made and the results are analysed, both from a mathematical and from a physical point of view. Various simplified computation methods are considered, most of which yield no satisfactory results when the advective influence of the secondary flow on the main velocity is important. Only a method based on similarity approximation sufficiently accurate to be applied further.