A novel spatial model for extreme events is proposed. The model may for instance be used to describe the occurrence of catastrophic events such as earthquakes, floods, or hurricanes in certain regions; it may therefore be relevant for, e.g., weather forecasting, urban planning, and environmental assessment. The model is derived from the following ideas: The above-threshold values at each location are assumed to follow a generalized Pareto (GP) distribution. The GP parameters are coupled across space through Markov random fields, in particular, thin-membrane models. The latter are inferred through an empirical Bayes approach. Numerical results are presented for synthetic and real data (related to hurricanes in the Gulf of Mexico). © 2012 IEEE.