The response of engineering structures is often sensitive to uncertainty in the system properties. The information on the uncertain parameters is frequently incomplete, limited to experts’ opinion, based on previous knowledge, or a combination of those. There have been recent advances in building mathematical models of structures, which combine nonparametric probabilistic and parametric (probabilistic or nonprobabilistic) models of uncertainty. Here, several strategies for establishing the response of random systems whose uncertainties are described by parametric probabilistic and nonprobabilistic approaches in combination with a nonparametric probabilistic approach are presented. The proposed strategies are illustrated by analyzing a built-up plate structure.