This paper presents a method for predicting the slamming pressure distribution over the ship surface of the two-dimensional arbitrary shape. The method is derived from the similar procedure developed by V. H. Wagner for a symmetric wedge penetrating the water surface, using the expanding flat plate approximation. The proposed method takes account of the piled up water at the free surface near the impinging body which is relevant to the pressure distribution and the peak value. For practical purposes, simple formulas are developed to estimate the maximum peak pressure on the surface of unsymmetrical wedges. Equations for the slamming of cone-shaped bodies are also shown in the appendix which are a little different from those derived by S. L. Chuang.