Lagrangian vortex methods of simulating the vortex shedding which occurs at the bilges and sharp edges of floating bodies under oscillatory flow conditions due to incident waves and motion of the body in response are presented. Local forces are taken from discrete vortex simulations of the flow around an isolated edge representing the bilge section of the hull. Both the classical, meshless, potential flow vortex method and a vortex-in-cell viscous simulation are used. The flow around the bilge of a typical long floating hull in beam waves is treated on a sectional basis and the isolated edge results are matched to the outer threedimensional wave potential flow provided by a standard surface panel method. The advantage of this matching procedure is that the more computationally expensive vortex flow simulation is limited to the local bilge section for which universal results may be computed whereas the large scale wave-hull interaction which extends out many hull- or wave-lengths from the body is solved by the less computationally intensive panel method. This procedure thus provides an efficient method replacing empirical vortex damping coefficients, as presently used, by a more rational method based on flow physics. Results for regular waves generating sinusoidal flows around right angle edges, edges fitted with flat plate bilge keels and rounded edges are presented and some comparisons made with measured data from laboratory wave tank tests and results of full Navier-Stokes simulations.