Model-scale experiments were conducted to investigate the non-linearities associated with the Vertical Bending Moment (VBM) of a rigid container vessel in irregular waves. Long-duration runs ( ≃ 25 hours of data in full scale) were performed to allow the calculation of statistically meaningful extreme values of hogging and sagging on five different sea-states (from Hs = 6 m up to Hs = 17 m).The model tests are presented in detail, and sampling errors are estimated. It is found that the ratio between linear and non-linear VBM (the so-called non-linear factor) can be modeled as a function of the linear value only. For a given linear value, the non-linear correction is the same, whatever the sea state. This observation, new in the fully non-linear case, is very valuable as it opens the door to efficient design assessment methodologies such as increased design sea state or design waves.