The influence of unforeseen, extreme weather in construction works usually impacts productivity, causes significant project delays and constitutes a frequent source of contractor's claims. However, construction practitioners cannot count on sound methods for mediating when weather-related claims arise, nor harnessing the influence of weather variability in construction projects. Building on the few most recent quantitative studies identifying those key weather agents and levels of intensity that affect some standard building construction activities, a new stochastic model that processes and replicates the spatio-temporal variability of combined weather variables is proposed. This model can help anticipate weather-related project duration variability; improving construction productivity by selecting the best project start date; and objectively evaluating weather related claims. A two-building construction case study using different Spanish locations is used to demonstrate the model. The results showed that ignoring the influence of weather can lead to an extension of 5-20% longer project duration compared to planned.