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A spilling breaker model (SBM) is implemented in an existing two-dimensional (2D) numerical wave tank (NWT), based on fully nonlinear potential flow (FNPF) theory and the boundary element method (BEM), in which an absorbing surface pressure is specified over the crest of impending breaking waves (detected based on a maximum front slope criterion) to simulate the power dissipated during breaking. The latter is calibrated to match that of a hydraulic jump of parameters identical to local wave properties (height, celerity,. . .). Although this model is not aimed at being fully physical in the surfzone, it allows more accurately simulating properties of fully nonlinear shoaling waves than standard empirical absorbing beaches (AB). After assessing the convergence with the discretization of 2D-NWT results for strongly nonlinear shoaling waves, simulations are first validated based on laboratory experiments for non-breaking and breaking waves, shoaling up a mild slope; a good agreement is found between both. The NWT is then used to compute fully nonlinear local (height, celerity, asymmetry) and integral (mean-water-level, radiation stress) properties of periodic waves shoaling over mild slopes. Discrepancies with standard results of wave theories are discussed in light of fully nonlinear effects modeled in the NWT. While only periodic waves are considered here, the SBM could be applied to shoaling irregular waves, for which the breaking point location will constantly vary, which would be advantageous compared to an AB fixed in space. For such cases, besides its more physical energy absorption, the SBM would allow better preventing wave overturning that may occur far from shore due to nonlinear wave-wave interactions and otherwise interrupt the FNPF-NWT simulations.