Equity issues and demand uncertainty are two important issues in the network design problem (NDP). Spatial equity in NDP is concerned with the benefit distribution among network users. By considering demand uncertainty, a more realistic evaluation of the network performance given a network improvement plan can be obtained. Two stochastic models that consider both spatial equity and demand uncertainty are formulated: an expected-value model and a chance-constrained model. Both models are solved by a simulation-based genetic algorithm procedure. The genetic algorithm is used to solve NDP, and stochastic simulation is used to simulate the demand uncertainty. The results of numerical experiments are provided to demonstrate the significance of the equity issue and demand uncertainty in NDP.