Bioceramics have rapidly emerged as one of major biomaterials in modern biomedical applications because of its outstanding biocompatibility. However, one drawback is its low tensile strength and fracture toughness due to brittleness and inherent microstructural defects, which to a certain extent prevents the ceramics from fully replacing metals used as load-bearing prostheses. This paper aims to model the crack initiation and propagation in ceramic fixed partial denture, namely dental bridge, by using two recently developed methods namely continuum-to-discrete element method (CDEM) in ELFEN and extended finite element methods (XFEM) in ABAQUS. Unlike most existing studies that typically required prescriptions of initial cracks, these two new approaches will model crack initiation and propagation automatically. They are applied to a typical prosthodontic example, thereby demonstrating their applicability and effectiveness in biomedical applications.