Natural materials such as bone and the nacre of some seashells are made of relatively weak building blocks and yet often exhibit remarkable combinations of stiffness, strength, and toughness. Such performances are due in large part to their brick and mortar architec-tures. Many effort s are devoted to translate these design principles into synthetic materials. However, much of the progress is based on trial-and-error approaches, which are time consuming and do not guarantee that an optimum is achieved. Modeling is an appealing alternative to guide the design and processing routes of such materials. However, the current analytical approaches cannot describe the extrinsic toughening mechanisms that takes place during crack propagation and are responsible for the remarkable properties of such materials. Here we show that the Discrete Element Method (DEM) can be used to predict the elastic and fracture behavior of brick and mortar materials and capture non-continuous phenomena such as multi-cracking. In contrast with most analytical shear-lag models, which only predict crack initiation, the model proposed here can also tackle crack propagation. DEM simulations are compared to analytical results with special attention to the shear transfer at the interface. The case of nacre-like alumina-a ceramic/ceramic brick and mortar composite with a brittle interface-is investigated to illustrate the potential of the method. We demonstrate in particular the importance of controlling the interface strength for further optimization of the mechanical properties. This method could be extended to predict and investigate the behavior of brick and mortar composites with a ductile interface, such as polymer/ceramic or metal/ceramic composites.