The ultimate strength assessment of ship hull structures in longitudinal bending is part of the ship design process, and in some cases, it stands for a limit state check in retrospect of a marine accident. The limit state violation is performed in a deterministic setting through the application of partial safety factors. In this work, we place the problem in a probabilistic setting that allows uncertainty quantification of the magnitude of the ultimate strength. The basic variables that control the problem mechanics are first identified and then a probability distribution is assigned. The general function that maps the basic random variables is highly non-linear and can be split into three different steps: 1) forward uncertainty propagation in each individual element stress-strain curve, 2) propagation of the element’s uncertainty to the curvature moment curve, and 3) identification of maximum strength. Monte Carlo simulations have been performed to tackle the problem at hand. Gaussian Process Regressors are employed in order to accelerate the calculation time.