Under the smart grid environments, Demand Response Resources (DRRs) as power system resources can effectively participate in and improve performance of electric systems. Congestion management is one of the technical challenges in which DRRs can play a significant role. Previously, congestion management is applied without considering the power system uncertainties. Therefore, a stochastic congestion management by means of a trade-off between DRRs and load shedding is proposed so that the outage of transmission lines and generating units are considered. In order to investigate the proposed framework, two types of Monte Carlo simulation methods, namely 1) ordinary and 2) lattice rank-1, are utilized and compared. Hence, Independent System Operator (ISO) can be able to relieve the existing transmission line congestion considering the uncertain network configuration. The proposed model is applied to the 24-bus Reliability Test System (RTS) and simulation studies are performed to examine the effectiveness and capability of the proposed framework.