Abstract: The phenomenon of the free overfall is studied here assuming the steady flow to be two-dimensional,irrotational and frictionless and accounting for the presence of gravity and two free curvilinear boundaries.The boundary integral equations for calculating 2-D potential free overfall flow with both free surfaces are derived by using the Riemann-Hilbert mixed boundary problem technique of analytical function.The numerical calculation on the physical plane shows that this method has the advantage of fast convergence with small calculating quantity and high accuracy,and applicable to the complex shaped boundary without special requirement to the initial inputted value.Comparison with the experimental data indicates the present computations allow fair determination of all flow quantities with high accuracy.