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A hybrid continuum-discontinuum method is introduced to model the rock failure process in Brazilian tensile strength (BTS) test. The key component of the hybrid continuum-discontinuum method, i.e. transition from continuum to discontinuum through fracture and fragmentation, is introduced in detail. A laboratory test is conducted first to capture the rock fracture pattern in the BTS test while the tensile strength is calculated according to the peak value of the loading forces. Then the proposed method is used to model the rock behaviour during BTS test. The stress propagation is modelled and compared with those modelled by finite element method in literatures. In addition, the crack initiation and propagation are captured and compared with the facture patter in laboratory test. Moreover, the force-loading displacement curve is obtained which represents a typical brittle material failure process. Furthermore, the stress distributions along the vertical direction are compared with the theoretical solution. It is concluded that the hybrid continuum-discontinuum method can model the stress propagation process and the entire rock failure process in BTS test. The proposed method is a valuable numerical tool for studying the rock behaviour involving the fracture and fragmentation processes.