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Extreme rainfall events can be considered a natural manifestation of the environment in which they are embedded and foreknowledge about their future behavior is very important, especially for decision makers. In this context, we aimed to explore the future behavior of extreme rainfall intensity through numerical simulations with the ETA model. The model was forced with a scenario of high greenhouse gas emissions for the middle of the 21st Century as described for A1B emission scenario. We detailed the main changes in accumulated rainfall produced by heavy events, very heavy events and rare events over a broad area of South America with a focus on the tropical sector. The methodology applied here is capable of separating extreme events and establishing the quantity of rainfall yielded by them. We have found that in the near future (2041-2050) rare events will tend to increase over the Amazon basin, followed by reductions in heavy and very heavy events. Conversely, heavy, very heavy and rare events are expected to decline over north-east Brazil. Furthermore, increases were found for heavy, very heavy and rare events over southern Brazil.