This paper analyzes the impacts of flexible demands on day-ahead market outcomes in a system with significant wind power production. We use a two-stage stochastic market-clearing model, where the first stage represents the day-ahead market and the second stage represents the real-time operation. On one hand, flexibility of demands is beneficial to the system as a whole since such flexibility reduces the operation cost, but on the other hand, shifts in demands from peak periods to off-peak periods may influence prices in such a way that demands may not be willing to provide flexibility. Specifically, we investigate the impacts of different degree of demand flexibility on day-ahead prices. A number of scenarios modeling the uncertainty associated with wind production at the operation stage, and nonconvexities due to start-up costs of generators and their minimum power outputs are taken into account.