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Recent years have seen an increase in demand for the demolition of obsolete and potentially hazardous structures, including reinforced concrete (RC) structures, using blasting techniques. However, because the risk of failure is significantly higher when applying blasting to demolish RC structures than mechanical dismantling, it is critical to achieve the optimal demolition design and conditions using blasting by taking into account the major factors affecting a structure’s demolition. To this end, numerical analysis techniques have frequently been used to simulate the progressive failure resulting in the collapse of structures. In this study, the three-dimensional (3D) combined finite discrete element method (FDEM), which is accelerated by a parallel computation technique incorporating a general-purpose graphics processing unit (GPGPU), was coupled with the one-dimensional (1D) reinforcing bar (rebar) model as a numerical simulation tool for simulating the process of RC structure demolition by blasting. Three-point bending tests on the RC beams were simulated to validate the developed 3D FDEM code, including the calibration of 3D FDEM input parameters to simulate the concrete fracture in the RC beam accurately. The effect of the elements size for the concrete part on the RC beam’s fracture process was also discussed. Then, the developed 3D FDEM code was used to model the blasting demolition of a small-scale RC structure. The numerical simulation results for the progressive collapse of the RC structure were compared to the actual experimental results and found to be highly consistent.