Supplier selection is one of the significant topics in Supply Chain Management (SCM). One of the techniques that can be used for selecting suppliers is Data Envelopment Analysis (DEA). In this study, to handle uncertainty in supplier selection problem, a new Russell model in the presence of undesirable outputs and stochastic data is developed. This study proposed a deterministic equivalent of the stochastic model and convert this deterministic problem into a quadratic programming problem. This quadratic programming problem is then solved using algorithms available for this class of problems. A numerical example is presented to demonstrate the applicability of the proposed approach.