The object of this study was to use the relaxation method to find the solution of cavity flow past a two-dimensional roughness element in an open channel with gravity effect included. The method developed is based on an inviscid, irrotational and incompressible flowfield, using a finite-difference representation with stream functions as dependent variables. A computer program is developed to adjust free boundaries systematically and to facilitate numerical computation. The Helmholtz-Kirchhoff cavity model is used in this study, with sixteen primary cases analyzed. The computer results are plotted and the computer listing is given. From the results, it is found that the Helmholtz-Kirchhoff model is not applicable because no finite length of cavity can be obtained. Finally, the use of the Riabouchinsky model is recommended.