Integrated assessment models (IAM) study the interlinkages between human and natural systems and play a key role in assessing global strategies to reduce global warming. However, they largely neglect the role of materials and the circular economy. With the Plastics Integrated Assessment model (PLAIA), we included plastic production, use, and end-of-life in the IAM IMAGE. PLAIA models the global plastics sector and its impacts up to 2100 for 26 world regions, providing a long-term, dynamic perspective of the sector and its interactions with other socioeconomic and natural systems. This article summarizes the model structure, mathematical formulation, assumptions, and data sources. The model links the upstream chemical production with the downstream production of plastics, their use in different sectors, and their end of life. Therefore, PLAIA can assess material use and emission mitigation strategies throughout the whole life cycle in an IAM, including the impacts of the circular economy on mitigating climate change. PLAIA projects plastics demand, production pathways and specifies the annual plastic waste generation, collection, and the impact of waste management strategies. It shows the fossil and bio-based energy and carbon flows in product stocks, landfills, and the emissions in production and at the end of life. • We included plastics production, use, and waste management into an Integrated Assessment Model (IAM). • Our model PLAIA provides a long-term, dynamic perspective of the global plastics sector until 2100 and its interactions with other sectors and the environment. • PLAIA can assess the impact of material use and emission mitigation strategies throughout the whole life cycle of plastics.