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Fully nonlinear water wave problems are solved using Eulerian-Lagrangian time stepping methods in conjunction with a desingularized approach to solve the mixed boundary value problem that arises at each time step. In the desingularized approach, the singularities generating the flow field are outside the fluid domain. This allows the singularity distribution to be replaced by isolated Rankine sources with the corresponding reduction in computational complexity and computer time. A moving boundary technique is applied to eliminate the reflection waves from limited computational boundaries. Examples of the use of the method in three-dimensions are given for the exciting forces acting on a modified wigley hull and Series 60 are presented. The numerical results show good agreements with those of experiments.