- The effects of uniform steady currents (or small forward velocity) on the interaction of a large three-dimensional body with waves are investigated by a time-domain higher-order boundary element method (THOMEM). The current speed is assumed to be small so that the viscous effects and the steady wave system generated by currents are insignificant. Using regular perturbation with two small parameters and associated with wave slope and current velocity, respectively, the boundary value problem is decomposed into the zeroth-order steady double-body-flow problem at O() with a rigid-wall free-surface condition and the first-order unsteady wave problem with the modified free-surface and body-boundary conditions expanded up to O(). Higher-order boundary integral equation methods are then used to solve the respective problems with the Rankine sources distributed over the entire boundary The free surface is integrated at each time step by Adams-Bashforth-Moulton method. The Sommerfeld OHanski radiation condition is numerically implemented to absorb all the wave energy at the open boundary To solve the so-called corner problem, discontinuous elements are used at the intersection of free-surface and radiation boundaries. Using the developed numerical method, wave forces, wave field and run-up, mean drift forces and wave drift damping are calculated.