Fully nonlinear monochromatic wave three-dimensional body interactions are studied with and without the presence of steady uniform currents. The mixed initial boundary value problem is set-up in a numerical wave tank (NWT) and solved by an indirect desingularized boundary integral equation method (DBIEM). The Laplace equation is solved at each time-step and time-dependent nonlinear free surface boundary conditions are simultaneously integrated by a mixed Eulerian±Lagrangian (MEL) method. A pistontype wave maker is used for generating the incident waves and a steady current is imposed everywhere in the computational domain at t 0 . A spatially varying sponge layer on the free surface is devised to dissipate the outgoing waves. The resulting in¯uence coecient matrix is divided into sub-matrices by domain decomposition technique and solved simultaneously by block line Jacobi method (BJM). A specially devised preconditioning matrix is used to accelerate the convergence rate of the matrix equation by obtaining the minimized condition number of the in¯uence coecient matrix. Computations are performed for the nonlinear diractions of steep monochromatic waves by a truncated vertical cylinder both without currents and in the presence of uniform coplanar or adverse currents. A / n -type adaptive beach is developed and its performance compared with some beaches in the literature. Results of NWT simulations are compared with the ®rst-order potential theory (Buchmann et al.,