Aim of this paper is to present a mathematical description of the flow profile in a river of which the discharge decreases gradually due to percolation. Subject to assumptions (uncurved, prismatic channel with fixed, flat bottom and constant slope, uniform velocity distribution) two ordinary differential equations can be derived, one describing the depth and the other the discharge, both as a function of the place. In determining the boundary conditions the singular points of these equations play an important part. In order to verify the theoretical approach, model experiments were carried out in a laboratory flume. The main conclusion is that the theoretical results are very sensitive to the accuracy with which the permeability of the bottom is determined.