In this paper, we study the problem of two-dimensional free surface flows past an inclined plate of an infinite length. The Riabouchinsky model is considered. The fluid is assumed to be inviscid and incompressible and the flow to be steady and irrotational. For this study, the effects of gravity and surface tension are negligible. This problem is solved by using two methods. The first method allow us to compute analytical solution by employing Schwarz-Christoffel mapping. The other is numerically using the series truncation method. The obtained results showed a good agreement between the numerical solution and the exact solution.