To simulate the processes of crack initiation and propagation in rock-like materials under static and dynamic loading conditions, a HFDEM(hybrid finite-discrete element method) was proposed. The HFDEM addresses the limitation of the Y2D model, which can only simulate single cracks, and incorporates an empirical relationship between the dynamic and static strengths of rock to better account for the effects of dynamic disturbances. The proposed method was applied to quasi-static Brazilian splitting tests and dynamic asymmetric three-point bending tests to analyze the processes of crack initiation and propagation, as well as the influence of loading rates on rock fracture behavior. The results demonstrate that HFDEM effectively integrates the advantages of finite element and discrete element techniques, accurately simulating the mechanical behavior of rock both before and after failure, and enabling the transition from a continuum to a discontinuum state. Furthermore, comparisons with analytical solutions and fracture patterns from Brazilian splitting tests validated the accuracy of HFDEM. Preliminary analyses also revealed the effects of loading rates on the dynamic fracture process and fracture toughness of rock.