In this chapter ‘Green function methods’ and all following chapters, the three-dimensional flow around the ship is computed to determine forces and moments caused by fluid pressure, thus avoiding the approximations inherent in strip methods. In this chapter, central to computing this flow is the Green function: the potential of a pulsating source under a free surface, at which it generates waves. If the source is not fixed, but translating relative to the fluid, numerical problems in computing this Green function are large; therefore, here this flow is approximated from that of a non-moving pulsating source. The sources are continuously distributed over ‘panels’ covering together the underwater ship hull. In each panel, the source density is determined such that there is no flow through the ship hull at all panel centers. The chapter describes also how to take account of the nonlinear effect of fluid pressure between the instantaneous and the average waterline.