In this work, we propose a methodology to predict the total cost of a natural catastrophe shortly after itsoccurrence. Thanks to a large database provided through a partnership with Federation Francaise d'Assurance,we manage to have access to a very large volume of claims (our database covers over 70% of the market). Usingmeteorological data, we measure the intensity of an event. Socioeconomic data provided by INSEE (French publicstatistical organization) allow to combine this information with a better knowledge of the exposure. In this workwe propose the application of dierent machine learning methods to handle this big volume of data, from sparseGeneralized Linear Models (Lasso and Elastic-Net penalties) to Random Forests.