Abstract: For the purpose of numerical simulation of transition process from continua to discontinua and even to structural collapse, the fracture of quasi-brittle materials such as concrete and rock under tensile state is analyzed by rotating smeared-crack model and discrete crack model based on the deformable distinct element method (DEM). The models are then applied to analyze the problems of uniaxial tension and three-point bending beam test. The comparison between experimental and numerical results shows that the models are able to appropriately predict the load-displacement response of the beam under uniform fracture energy. The discrete crack model is not only capable of obtaining the load-displacement curve of the entire fracture process but also of simulating the collapse behavior when the system partially or completely reaches failure.