This study addresses to which degree the circular economy may resolve the resource challenges of the future. The results imply that a circular economy alone will not make the world sustainable. All business-as-usual scenarios with improvements show peak behaviour, end up with resource exhaustion, and fail to achieve sustainability. The results indicate that a circular economy can delay the core problem and soften the effects, but it will not prevent it. High losses of resources and delays during the implementation and the lack of available renewable substitutes for finite resources lead to increasing extraction rates and energy losses. While energy and materials’ recovery rates improve, there will always be a loss of energy and resources. Efficiency improvements in a system that requires growth will only delay the risk of system malfunction. The models show that a system based on constant growth outgrows any finite supply capacity. To achieve a sustainable society, strategies involving system change are needed. The study uses Integrated Assessment Model WORLD7 to describe the world system behaviour and help identify the system’s possible intervention points. Without models, such a study would not have been possible, showing that models are a required part of policy development.