In this paper, we present a non-local approach to fracture modeling in brittle or quasibrittle materials and its finite element implementation. The proposed fracture model is constructed on the basis of the conventional maximal principal stress criterion for uniform tensile loads and the Griffith-Irwin criterion for crack propagation prediction. Consequently, the proposed fracture criterion can be used to predict both the crack initiation and the crack growth. Moreover, we also showed that when the element size is much smaller than the characteristic length scale of the material, the proposed fracture model is mesh-independent. By using the proposed model, we carried out detailed numerical simulations on cracking process of ceramic materials subjected to thermal shock loading. The comparison with the experimental results shows that the periodic and hierarchical structure of the crack pattern is faithfully reproduced by the numerical simulations. (C) 2014 Elsevier Ltd. All rights reserved.