Exceeding the strength of the bone tissue results in a break in its structural continuity and ultimately in a fracture. The broken bone is usually stiffened with the help of external fixators or osteosynthesis plates. Bone fixation plates are mainly made of titanium alloy or stainless steel. However, they are characterized by a relatively high stiffness modulus compared to bone tissue, which can lead to a formation stress shielding effect and cause the additional pain for the patient and improper bone healing process. Therefore, the good solution to overcome this drawback could be to manufacture osteosynthesis plates from polymer composites or functionally graded materials (FGM) with properties close to bone tissue. A good polymer material for the matrix part of the composite seems to be PEEK (polyetheretherketone), which is welcomed for biomedical applications and has a high resistance to mechanical damage. Therefore, the aim of this work was to model a carbon fiber-reinforced PEEK composite plate and to estimate the stiffness of the fractured tibia stabilization system with the help of numerical simulations. The different boundary conditions of the analysis were taken into account, including loads dependent on the degree of bone healing, the composite structure and the shape of the plate model. The results obtained were compared with the measured data from analyses of conventional materials (titanium alloy, stainless steel) and FGM Ti-HAP. The numerical analysis showed that the osteosynthesis plate made of the CF-PEEK polymer composite could provide adequate fixation of the fractured bone. This solution resulted in a reduction of stresses and deformations in the bone-plate system compared to conventional metal plates. The studies also indicated the need for further analysis to optimize the structure and shape of the composite plate.