A nonlinear numerical wave tank has been developed using a three-dimensional higher order boundary element method (HOBEM). For this, simple (Rankine) sources are distributed on the free surface and other boundaries. The resulting boundary integral equation is repeatedly solved at each time step using a predictor-corrector time integration scheme. The instantaneous free surface points are calculated by the Eulerian scheme assuming that the free surface is single-valued. For the corners and edges of the wave tank, discontinuous boundary elements are employed, and at the open boundary a special form of Sommerfeld/Orlanski open boundary condition is used. Numerous numerically simulated linear and nonlinear waves are compared with theoretical input waves. In particular, very steep Stokes 3rd-order-like long-crested irregular waves are successfully simulated using our nonlinear numerical wave tank.