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Demand side load shift has re-emerged as an important tool to solve the problems accompanying the restructuring of power systems, such as capacity shortage, transmission congestion, electricity price volatility and possible reduced system reliability. A methodology to determine demand side load shift is developed to enhance reliability and to reduce nodal price volatility of restructured power systems. In restructured power systems, the conventional "same for all customers" electricity price is replaced by nodal prices. Electricity prices will interact mutually with demands. This interaction is known as demand response. Demand response is modeled using demand-price elasticity matrix which includes self- and cross-elasticities. The demand side load shifts under N-2 random system contingencies are determined using demand-price elasticity. Then the overall stochastic demand side load shift is calculated using the determined demand side load shifts under random contingencies and their probability. Reliability enhancement and nodal price reduction of restructured power systems due to stochastic demand side load shift are investigated using optimal power flow (OPF) and reliability evaluation techniques. A small but comprehensive reliability test system, RBTS, is used to illustrate the concepts, and simulation results show that stochastic demand side load shift is an efficient tool to reduce nodal price volatility and enhance system and nodal reliability of restructured power systems.