<p>Real-life transport operations are often subject to uncertainties in travel time or customers’ demands. Additionally, these uncertainties greatly impact the economic, environmental, and social costs of vehicle routing plans. Thus, analysing the sustainability costs of transportation activities and reliability in the presence of uncertainties is essential for decision makers. Accordingly, this paper addresses the Sustainable Vehicle Routing Problem with Stochastic Travel times and Demands. This paper proposes a novel weighted stochastic recourse model that models travel time and demand uncertainties. To solve this challenging problem, we propose an extended simheuristic that integrates reliability analysis to evaluate the reliability of the generated solutions in the presence of uncertainties. An extensive set of computational experiments is carried out to illustrate the potential of the proposed approach and analyse the influence of stochastic components on the different sustainability dimensions.</p>