The Future Circular Collider (FCC) study is a feasibility study launched by CERN to propose different concepts for circular colliders in the post-LHC era. A core part of the study focuses on FCC-hh, a high energy hadron-hadron collider with a circumference of nearly 100 km and a foreseen center of mass beam energy of 100 TeV. The energy stored in each proton beam at 50 TeV is approximately 8.3 GJ, more than 20 times that of LHC. This implies a large damage potential of the beam and emphasises the need of detailed failures studies at all stages of the design. Injection and extraction processes are of particular interest regarding machine protection as most of the occurring failures have a very fast impact on the beam and thus require immediate reaction and passive protection. Consequently, the design of the FCC-hh injection and extraction system is strongly driven by machine protection and reliability considerations. In this thesis, failure cases of the injection and extraction system are identified and evaluated in detail. A first design of the injection protection scheme is proposed and simulations to validate the protection efficiency presented. For the extraction system, several design options including different hardware choices and abort strategies are worked out and evaluated regarding machine impact, safety and availability. Required hardware specifications to reduce the probability and mitigate the impact of the mentioned failure cases are discussed and an optimized design for the FCC-hh extraction system is proposed.