The Special Issue contains six peer -reviewed papers. The papers cover various aspects of computational models of material failure which has been the topic of this special issue. The prediction of fracture and failure of engineering systems and materials has been of interest for many years. Methods to predict material failure can be categorized into continuous approaches to fracture and discrete crack approaches. Gradient-enhanced models, non-local models and phase field models are among the most common representatives of the first class of methods while the extended finite element method (XFEM), meshfree methods, peridynamics or efficient remeshing techniques belong to the latter type. The published papers cover several new methodological aspects of computational methods such as the cracking element method presented by Sun et al., the coupled SFEM-SBFEM by Surendran et al. or new fracture criteria in the context of peridynamics suggested by Zhao. Some contributions also focus on application of computational methods to predict material failure in concrete.