In engineering, design optimization is often performed in a virtual environment using finite element models. These models approximate the solution of partial differential equations. However, when only partial or uninformative data is available to estimate the model parameters, the results obtained by numerical approximation can diverge significantly from real structural behavior. Interval analysis has proven to provide robust bounds on the structure's performance under such limited data. Performing an interval analysis typically requires a global optimization procedure to calculate the interval bounds on the output side of a computational model. The main issue of such a procedure is that it requires a large number of full-scale model evaluations. Even when simplified approaches such as the vertex method are applied, the required number of model evaluations scales combinatorially with the number of input intervals. This becomes especially problematic for highly detailed numerical models containing thousands or even millions of degrees of freedom. Recently, the authors presented a multilevel Quasi-Monte Carlo framework for interval analysis which significantly reduces computational costs for medium to high number of input intervals and effectively breaks the so-called “curse of dimensionality” (Callens, 2022). In this approach, the input intervals are first transformed into Cauchy random variables (Kreinovich, 2004). Based on these variables, a multilevel Quasi-Monte Carlo sampling is designed. Finally, the corresponding model responses are post-processed to estimate the intervals on the output quantities with high accuracy (callens, 2022). This work extends the Quasi-Monte Carlo framework towards interval analysis for non-linear input-output relationships. Hereto, the input intervals are split into smaller sub-intervals with linear input-output responses. For these sub-intervals interval analysis is performed. Then the maximum and minimum response found from all sub-interval analyses is an estimate of the real output interval. The Quasi-Monte Carlo for intervals analysis is applied to a numerical model with a non-linear input-output relationship to compare the accuracy and computational cost.