Starting from a logarithmic main velocity profile, the vertical distribution of the secondary flow in a shallow curved channel is derived. The secondary circulation turns out to have one vertical and two horizontal components. The horizontal component in the main flow direction arises from the longitudinal acceleration of the main flow; the transverse horizontal component is due to the curvature of the main flow. In addition, a numerical method for the computation of the depth-averaged flow field and the bed shear stress (magnitude and direction) is developed. This model has great flexibility of allowable channel geometry. Its results agree better with experimental data if the bed is not flat than in case of a flat bed.