Nonwoven materials, characterized by a random fiber structure, are essential for various applications including insulation and filtering. An industrial long-term goal is to establish a framework for the simulation-based design of nonwovens. Due to the random structures, simulations of material properties on fiber network level are computational expensive. We propose a predictive model hierarchy for inferring an important material property—the nonwoven tensile strength behavior. The model hierarchy is built using regression-based approaches, including linear and polynomial models, which provide interpretable results. This allows for significant speedup (six orders of magnitude) over the conventional simulations, while achieving good prediction results ( \(R^2=0.95\) ). The proposed models open the application to nonwoven material design, as they provide accurate and cost-effective surrogates for predicting material properties. In this way, our work serves as a proof of concept.