A combination of sustainability-related regulations and increased demand from stakeholders has pressed firms to adequately address sustainability-related risks. This issue is particularly important, and challenging, for the freight transportation sector due to its exposure to a large number of inherent sustainability risks. Despite the growing significance of sustainability risks, there is a lack of research related to sustainability risk management, which may be due to the difficulties in identifying and evaluating sustainability risks. We aim to fill this research gap by identifying, measuring and modelling sustainability risks in the context of freight transportation.Our research makes three primary contributions. First, we introduce the concept of a sustainability risk index (SRI) to understand the risk exposure of freight transportation systems (FTSs) in the context of India, an emerging market. The SRI is a mathematical tool used to measure sustainability risks and to quantify a firm's exposure to sustainability-related risks.Second, we propose an integrated two-phase model based on an interval 2-tuple linguistic (ITL) model and a digraph matrix approach (DMA) to calculate the SRI. In contrast to other existing techniques, the proposed approach can effectively deal with uncertain and incomplete linguistic assessments without suffering a loss of information. Third, we propose a framework for calculating both the disruption scores and influencing power of sustainability risks to evaluate the associated criticality and triggering power. For a robustness check, we also conduct a sensitivity analysis of the impact of risk variations on the SRI. Unlike conventional perceptions, our results show that organisational and governmental risks, which are mostly behavioural and skills-induced, are more significant for sustainable FTSs compared to financial risks. Our research helps the managerial community in the freight transportation sector in emerging markets to engage in more informed decision-making to proactively mitigate sustainability risks, which have potentially devastating financial, environmental and societal impacts.