Managers at various echelons of supply chains are continuously faced with problems of examining and improving supply chain processes with the aim of improving productivity and customer service level, while reducing emissions and total costs simultaneously. This study is aimed at presenting the trends in sustainable manufacturing supply chain modelling in order to establish the modelling approaches which have predominantly been used for improving manufacturing supply chains from years 2010 to 2020. The study employs the systematic literature review methodology for reviewing articles published within the 11-year period. We proffer a classification approach for manufacturing supply chain models, grouping these models into mathematical models, simulation models, hybrid models, and their subcategories. The results showed that though there is a rising trend in the use of simulation and hybrid models, mathematical models have been used more for sustainable manufacturing supply chain modelling. The rise in the use of simulation and hybrid models can be explained by the fact that these models tend to handle uncertain and stochastic data better than mathematical models, which perform better with deterministic data. This research will aid other researchers in recognising the current gaps in manufacturing supply chain modelling in order to identify future research directions.