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 lime-dependent nonlinear free surface boundary conditions are simultaneously integrated by a mixed Eulerian-Lagrangian (MEL) method. A piston-type 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 influence coefficient 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 influence coefficient matrix. Computations are performed for the nonlinear diffractions of steep monochromatic waves by a truncated vertical cylinder both without currents and in the presence of uniform coplanar or adverse currents. A phi (n)-type adaptive beach is developed and its performance compared with some beaches in the literature. Results of NWT simulations are compared with the first-order potential theory (Buchmann et al., Proceedings of the Seventh International Offshore and Polar Engineering Conference, Honolulu, Hawaii, USA, 1997), second-order diffraction theory [Kim and Yue, J. Fluid Mech. 200 (1989) 235-264], modified marker and cell (MAC) method (Park et al., International Journal for Numerical Methods in Fluids 29 (1999) 685-703) and the experimental and second-order potential theory results of Mercier and Niedzwecki [Proceedings of the Seventh International Conference on Behavior of Offshore Structures, vol. 2, TX, USA, 1994, pp. 265-287]. (C) 2001 Elsevier Science B.V. All rights reserved.