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An advanced numerical scheme for computing the free surface flow about a ship is presented. The present approach is a higher order panel method which employs a parabolic quadrilateral as a basic element. It can represent an actual curved ship hull surface more accurately with a smaller number of panels than is possible with a flat panel approximation. Singularity strength can vary linearly or quadratically across the panel. A sample unbounded flow problem with an analytical solution was considered first to validate the present approach and examine the characteristics of accuracy and convergence compared with those of the conventional low-order approaches (constant source strength across flat panel). The Wigley hull and the Series 60, C sub B=0.60 hull, which have been studied extensively, were selected for sample free surface flow computations. Comparisons between calculated and experimental results show good agreement. A modified body boundary condition was suggested to simulate a dry transom stern numerically, and calculated results show good correspondence with test data. Keywords: Ship hulls; Wave profile; Wave-making resistance; Higher-order panel method.