In construction projects, contingency reserves have traditionally been estimated based on a percentage of the total project cost, which is arbitrary and, thus, unreliable in practical cases. Monte Carlo simulation provides a more reliable estimation. However, works on this topic have focused exclusively on the effects of aleatoric uncertainty, but ignored the impacts of other uncertainty types. In this paper, we present a method to quantitatively determine project cost contingency reserves based on Monte Carlo Simulation that considers the impact of not only aleatoric uncertainty, but also of the effects of other uncertainty kinds (stochastic, epistemic) on the total project cost. The proposed method has been validated with a real-case construction project in Spain. The obtained results demonstrate that the approach will be helpful for construction Project Managers because the obtained cost contingency reserves are consistent with the actual uncertainty type that affects the risks identified in their projects.