Measuring sustainability as an efficient tool to achieve sustainable development and improve economic, social, and environmental aspects is always fraught with complications. Consequently, the identification of a suitable method capable of evaluating and recognizing the strengths and weaknesses across these dimensions is paramount. Given that data in many real-world applications exist in uncertain and random forms, the primary aim of this paper is to present a model for evaluating sustainability within a stochastic environment using the technique of data envelopment analysis (DEA). The proposed model is non-radial and incorporates undesirable outputs, enabling the assessment of overall sustainability as well as each of the economic, social, and environmental dimensions simultaneously. This multi-dimensional evaluation capability is a key advantage of the proposed model. Additionally, the proposed model is based on input excesses and output shortfalls. Another notable advantage is the incorporation of the assumption of managerial disposability when dealing with undesirable outputs. To illustrate the proposed sustainability model across economic, social, and environmental dimensions, data from 59 countries spanning Africa, Europe, North America, and Asia are analyzed and evaluated within a stochastic environment.