<p>Construction materials used for masonry units and mortar are typically quasi-brittle. The current research presents a computational framework to simulate fracture in these materials using the discrete element method. In this framework, the surface geometry is first discretized into a fine unstructured triangular tessellation, which is then extruded to form triangular blocks that constitute the 3D volume. The fine discretization enables modelling of the initiation, propagation and coalescence of cracking within the simulated materials. The ability of the proposed modelling approach to reproduce realistic fracture patterns is first evaluated using experimental results from the literature. The comparisons demonstrate that the proposed framework can be used to simulate Mode-I fractures in direct tension as well as mixed mode fractures under compression. The influence of block size on the crack pattern and global load–displacement predictions is systematically explored. The framework is then utilized to investigate the influence of pre-existing morphological irregularities on the fracture response. For this purpose, a custom algorithm is developed to introduce joined element clusters (to simulate stiff inclusions within the material) and voids (to simulate defects within the material) within the geometry. Results show that defects within the material, particularly in masonry mortar joints, act as crack initiators and significantly reduce load-carrying capacity, underscoring the importance of mortar integrity in structural performance. The examples highlight the framework’s potential to enhance the performance evaluation of masonry materials and structures.</p>