Increasing food waste, natural resource depletion, and climate change issues have forced plastic food packaging (PFP) companies to align their business strategies with sustainability aspects. At the same time, however, companies operating in the food packaging industry continue to face tensions while pursuing divergent sustainability goals simultaneously. Drawing on paradox theory, this study aims to examine paradoxical sustainability tensions in the PFP industry and propose potential resolution strategies to resolve diverse tensions arising from addressing competing social, economic, and environmental concerns simultaneously. To this end, we employed a qualitative research methodology and interviewed 15 senior corporate managers and consultants in the PFP industry. Based on the empirical data, we develop categories of sustainability tensions related to operations and supply chain, recycling, and external stakeholders associated with performing, organizing, learning, and belonging paradoxes. Further, we propose resolution strategies including multi‐stakeholder collaboration, research and innovation, circular economy, and use of integrated business strategies which are aligned with the acceptance, spatial separation, temporal separation, and synthesis approaches of the paradox theory. To the best of our knowledge, it is one of the early studies that embrace a paradox lens to investigate the sustainability tensions and resolution strategies in the PFP industry. Further, the study results could guide practitioners and policymakers in the PFP industry to comprehend underlying paradoxical sustainability tensions and promote resolution strategies to address divergent yet desirable economic, social, and environmental considerations simultaneously.