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This paper contains the results of the study on the development of fracture and crackpropagation in quasi-britle materials, such as concrete or rocks, using the Discrete Element Method(DEM). A new discrete element numerical model is proposed as the basis for analyzing the inelasticevolution and growth of cracks up to the point of gross material failure. The model is expected to predictthe fracture behavior for the quasi-britle material structure using the elementary aggregate level, theinteraction betwen aggregate materials, and bond cementation. The algorithms generate normal and shearforces betwen two interfacing blocks and contains two kinds of contact logic, one for connected blocksand the other one for blocks that are not directly connected. The Mohr-Coulomb theory has been used forthe fracture limit. In this algorithm the particles are moving based on the conected block logic until theforces increase up to the fracture limit. After pasing the limit, the particles are governed by the discreteblock logic. In seting up a discrete polygon element model, two dimensional polygons are used toinvestigate the response of an asembly of diferent shapes, sizes, and orientations with blocks subjectedto simple applied loads. Several examples involving asemblies of particles are presented to show thebehavior of the fracture and the failure process.