It is intended to solve a problem to determine the unknown wetted surface of free-running planing plate. Efforts from the view point of the perturbation method are paid to analyze both the near and far field of flow around a restrained planing plate with comparably large breadth such a wave-dozer, disregarding gravitational effects. Matching process of each height of water surface leads to a non-linear system of integro-differential equations to determine the distributions of both the wetted length and the apparent circulation around the plate. Serious solution of reduced single integral equation, still holding 3-dimensional characteristics but the so-called downwash effects, diverges from the assumed high aspect ratio solution because of the logarithmic non-linearity. The equation gains an insight into static stability in performance and the limitation in height to restrict the plate in exposure above still water. The obtained configuration of wetted surface draws well the behaviour of the spray root line crossing the hard chine, however it is unfortunately rather wide to coincide with the experimental one. Free-running condition is estimated.