The wave field of ships computed by a Rankine panel method is ‘extrapolated’ up to large distances from the ship. For deep water or shallow water of constant depth, a Fourier analysis of the waves within a small ‘analysis rectangle’ allows to determine the waves at other locations where the linear free-surface condition holds. The method is applicable also for a curved ship path. For shallow water of variable depth, a mild-slope wave propagation equation is solved by a finite-difference method separately for various wave frequencies.