Effects of external disturbances such as the population change on dynamics of water supply, power generation and environmental (WPE) systems have seldom been investigated. Following the WPE nexus profiled in the study of Feng et al. (2016), this study incorporated stochasticity of population, water supply and power generation into the modeling of the dynamical system in the Hehuang region of China, and further quantified resilience measures to understand the system's ability to withstand stochastic disturbances. First, the stochastic differential equations were used to improve the simulation of stochasticity in the WPE nexus. Next, the transient probability distribution functions (pdfs) of system variables, obtained by Monte Carlo simulation, were used to describe the evolutionary process of the system. Finally, the stationary pdfs of variables which reflect stable states of the system were derived to calculate four resilience measures. It is shown that: (1) The system approached a stable state after Year 2400 by calculating the L2 norm of the difference between transient and stationary pdfs. (2) The environmental system was identified as the most vulnerable subsystem because of its long convergence time. (3) The water supply system did not change greatly and it would remain stable at its current low level, i.e., water consumption per capita would be less than 80m³. The method adopted in this study is conducive to avoiding risk and the results provide valuable insights for regional management of a WPE nexus.