Within this work, a probability box approach is investigated to capture mixed aleatory and epistemic uncertainties within non-linear finite element method. The approach is applied to brittle damage problems regarding one and two input random fields. While random fields describe naturally aleatory uncertainty, the epistemic part is introduced by an interval-valued correlation length. The random field is discretized by Karhunen-Lo`eve expansion. To avoid the truncation error affecting the probability box, the truncation error is kept constant with regard to the different assumed correlation lengths. Outcome of interest are the probability boxes of the local and the global damage of a four-point bending simulation of a concrete beam. It is shown that the correlation length mainly affects the standard deviation but not the mean value of the outcome. Furthermore, despite the non-linearity of the problem, it can be shown that the probability box is described by the correlation length interval bounds only for this example.