Throughout their lifetime, infrastructure network systems face unplanned events that impose pressures on their integrity, functionality, and ability to deliver value. Most of the existing infrastructure is designed to deal with the challenges imposed by uncertain external phenomena. Authors from different backgrounds have identified flexibility, changeability, and adaptability as key attributes that modern systems should have to face uncertain scenarios. Specifically, flexibility is an ability that allows a system to be easily adapted when necessary. The concept of flexibility is compelling, but it is not clear how to measure the value it may provide. Determining how much to pay to introduce flexibility is an essential aspect of designing flexible systems, but the dependence of this value on the future evolution of the system results in a complex decision process. The sequential nature of the process can be modeled using multistage stochastic programming. The model explicitly considers the flexibility built into the network components as a decision variable at the initial stage. The model is tested in a generic infrastructure network that must meet a stochastic demand. The results show the relationship between the value of flexibility and the life-cycle costs at the construction and operation stages.