Nowadays, every business organization has to execute all decisions in a highly competitive and uncertain scenario for improving its performance. One of such decision that every organization has to undergo is to select best suppliers for timely delivery of good quality parts at minimum cost. Therefore, effective and cost-efficient supplier selection in a stochastic or uncertain scenario helps an organization in achieving its goal. Hence, this paper deals with the supplier selection problem under stochastic environment. In the present work, an attempt is made to model Stochastic Multi-objective Supplier Selection Problem (SMoSSP) applying chance constraint approach. The proposed model considers operational risks involving uncertainties-related supplier’s capacity, product demand, transportation and variable costs and lead time probability distributions. The SMoSSP is solved using non-preemptive goal programming and weighted aggregate function technique. To validate the proposed model data is generated randomly and solved in LINGO 10. Illustrative examples are presented to demonstrate the SMoSSP.