This contribution deals with the uncertainty quantification for applied nonlinear structural engineering problems, including high stochastic dimensions. A finite element problem with different material models is investigated. The efficiency, accuracy and convergence of sparse PCE are studied numerically and compared with Monte‐Carlo Simulation (MCS) for non‐linear structural analysis including elasto‐plastic and damage models. In both models, the Young's modulus is considered as random fields discretised by Karhunen Loeve Expansion (KLE). In the provided studies, sparse PCE converges fast and is highly efficient for linear elastic and elasto‐plastic material models. However, sparse PCE loses its effectiveness and exhibits lower accuracy for the damage material model.