Polyetheretherketone (PEEK), a biocompatibility tested material is rapidly gaining popularity in the medical implants industry. Hence, the investigation and understanding of the fracture properties of PEEK have garnered significant interest and importance. Computational simulations offer a cost-effective alternative to experimental studies while also providing valuable physical insights that may be challenging to obtain only through traditional experimental methods. This work aims to understand the fracture of the PEEK biomaterial due to presence of existing circular discontinuities in a geometry by using a variational formulation of an energy-based approach known as phase-field method (PFM). The formulation is briefly discussed and is applied to two common loading conditions in a square geometry having a circular hole with varying hole diameter. Further, geometries containing existing edge cracks and cracks associated with circular hole are also simulated. The method is validated by comparing results with existing literature. The results are analysed and the employability of the proposed method is discussed with an emphasis on biomedical applications.