With the increase of the concern from the public for environmental pollution and waste of resources, the value recovery through reuse, repair, remanufacturing and recycling from the end-of-use (EOU) and end-of-life (EOL) products have become increasingly important. Reverse logistics is the process for capturing the remaining value from the EOU and EOL products and also for the proper disposal of the non-reusable and non-recyclable parts. A well-designed reverse logistics system will yield both economic and environmental benefits, so the development of an advanced decision-making tool for reverse logistics system design is of significant importance. The paper presents a novel multi-product multi-echelon stochastic programming model with carbon constraint for sustainable reverse logistics design under uncertainty. Compared with the previous stochastic optimization models in reverse logistics system design, which mainly focuses on the expectation of the optimal value, this paper, however, emphasizes on both optimal value expectation and its reliability in decision-making. Due to this reason, a multi-criteria scenario-based risk-averse solution method is developed based on a latest research in order to obtain the optimal solution with high level of confidence. Later in this paper, the application of the model and the augmented solution method is illustrated and the managerial implications are discussed through the numerical experiment and sensitivity analysis. The result of the study shows that the model can be used for providing decision-makers with a deep insight into the relationship between profit and carbon emission requirement, understanding and resolution of the infeasibility caused by capacity limitation, the use of flexible manufacturing system in reverse logistics, and proper use of the government subsidy as a leverage in reverse logistics design.