Endoprostheses for interbody fusion should have not only biocompatibility and high strength characteristics, but also good visualization with additional research methods (CT, MRI). One such material is carbon. Aim: using mathematical modeling (the finite element method) to develop a model of the interbody prosthesis from a carbon-carbon composite and evaluate the stress-strain state of the vertebral body-implant system. Methods: models created in SolidWorks software. 18 design schemes with endoprostheses from a carbon-carbon composite were developed and studied. Bending load was carried out by angular displacements (2°), compressive — by applying a force of 500 N to the upper cubic element. Additional symmetry conditions were also simulated. Results: a parametric model of the biomechanical system of the lumbar spine was constructed. The smallest equivalent stresses were obtained in the design scheme M17, and the largest — in M13. In the bone elements of the systems, they did not exceed the ultimate strength limits for cortical (160 MPa) and cancellous (18–22 MPa) bones. Contact pressure and displacement are determined for all design schemes. Conclusions: as a result of the numerical values and distribution fields of the components of the stress-strain state in the elements of the studied systems, it was found that the use of the proposed endoprosthesis made of a carbon-carbon composite, the geometric parameters of which correspond to the design scheme M17, is effective for achieving additional stabilization in the system «vertebral body – implant».