Sustainable supply chain network design is a core area within supply chain management. Previous published research shows the application of various operations research methods and mathematical models. However, less focus was given to the environmental and social aspects and thus opens the road for further research. The present study put special attention to the food processing sector in India. Systematic literature review approach is followed to evaluate developments on quantitative models that address sustainability aspects in the supply chain of food sector. It is observed that heuristic models, optimisation models and expert system models are commonly used in earlier published papers. The present study employed ISM methodology and MICMAC analysis to indentify the contextual interrelationships between the leading barriers influencing sustainable supply chain network design. The dependent and independent variables identified from the study will help managers and decision makers successfully design sustainable network by eliminating the top level barriers. Conclusions are drawn which will serve as a practical solution to the researchers and decision makers.