Purpose Recently, sustainable supply chain management (SSCM) has generated significant interest and gained attention of practitioners and academics. The purpose of this paper is to explore different themes in the existing literature, which pertains to social sustainability (SS) in supply chains, to argue for the use of SS model and suggest further research directions. Design/methodology/approach In the study, the authors have undertaken extensive literature review (n = 171) and used thematic analysis to propose a model. Findings Through the extensive review and thematic analysis, the paper identifies eight themes, which include stakeholder pressure, sustainability culture, contingencies, sustainability practices, partnerships, drivers and barriers, sustainability performance and optimization, and develops a SS model called "five-factor sustainability model." Furthermore, a list of potential research directions for five-factor sustainability model is discussed. Research limitations/implications The research is an attempt to explore different themes related to SS in supply chain and develop a model that is also applicable to economic and environmental sustainability. Originality/value The paper offers a new approach to SSCM literature, arguing for five-factor sustainability model and providing further research directions. Moreover, this model will help sustainability scholars to position and integrate their research within social, economic and environmental sustainability literature.