Nonlinear wave forces on offshore structures are investigated. The fluid motion is computed using a Euler-Lagrange time-domain approach. Nonlinear free surface boundary conditions are stepped forward in time using an accurate and stable integration technique. The field equation with mixed boundary conditions that result at each time step are solved at N nodes using a desingularized boundary integral method with multipole acceleration. Multipole accelerated solutions require O(N) computational effort and computer storage, while conventional solvers require O(N2 ) effort and storage for an iterative solution and O(N3 ) effort for direct inversion of the influence matrix. These methods are applied to the three-dimensional problem of wave diffraction by a vertical cylinder.