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Modelling rainfall extremes and dry periods over the Southeast Asia (SEA) region is challenging due to the characteristics of the region, which consists of the Maritime Continent and a mountainous region; it also experiences monsoonal conditions, as it is located between the Asian summer monsoon and the Australian summer monsoon. Representing rainfall extremes is important for flood and drought assessments in the region. This paper evaluates extreme rainfall climatic indices from regional climate models from CORDEX Southeast Asia and compares them with the results of high‐resolution global climate models with a comparable spatial resolution from the HighResMIP experiment. Observations indicate a high intensity of rainfall over areas affected by tropical cyclones and long consecutive dry day periods over some areas in Indochina and the southern end of Indonesia. In the model simulations, we find that both coupled and sea surface temperature‐forced HighResMIP model experiments are more similar to the observations than CORDEX model results. However, the models produce a poorer simulation of precipitation intensity‐related indices due to model biases in the rainfall intensity. This bias is higher in CORDEX than in HighResMIP and is evident in both the low‐ and high‐resolution HighResMIP model versions. The comparable performances of HighResSST (atmosphere‐only runs) and Hist‐1950 (coupled ocean–atmosphere runs) demonstrate the accuracy of the ocean model. Comparable performances were also found for the two different resolutions of HighResMIP, suggesting that there is no improvement in the performance of the high‐resolution HighResMIP model compared to the low‐resolution HighResMIP model. [ABSTRACT FROM AUTHOR]