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Speleothem oxygen isotopes have been shown to exhibit a close relationship with summer insolation in the Northern Hemisphere, leading to the hypothesis that East Asian monsoon intensity is proportional to the summer insolation. This hypothesis, however, has been questioned because previous climate model simulations have been unable to simulate the observed large variation in precipitation or the precipitation isotope values, about a half of the variation in the entire modern tropical regions, in response to the insolation change due to the precession cycle. Here we show new results, using the fully coupled Geophysical Fluid Dynamics Laboratory model, that it is dynamically possible to have much higher precipitation during the high summer insolation period compared with the low summer insolation period in the East Asian monsoon region. We conclude that past East Asian monsoon intensity probably increased with increasing northern hemispheric insolation, given a large change in speleothem oxygen isotopes. Plain Language Summary: Speleothems from calcite caves draw attention because precise dating is possible using the U‐Th method, opening up a unique chance of studying the past hydrological cycle. The isotopic composition of Chinese caves shows a remarkably coherent pattern following the summer solar radiative flux in the Northern Hemisphere, particularly responding to the precesssional cycle, leading to the hypothesis that East Asian monsoon intensity is proportional to the summer insolation. However, because climate models were not able to simulate the direct precipitation response following the insolation over the East Asian monsoon region or the isotope variation, this interpretation of the speleothem data has been challenged. Our new results show that it is dynamically possible to have much higher precipitation (more than 100% increase locally) during the high summer insolation period compared with the low summer insolation period in the East Asian monsoon region, but unlike previous studies, our simulations use a fully coupled ocean model, emphasizing the importance of including the ocean dynamics in studying climate response. Key Points: It is dynamically possible to have much higher precipitation when summer insolation is high in the East Asian monsoon regionFully accounting for ocean circulation is important in simulating East Asian monsoon changeEast Asian monsoon intensity probably increases with increasing northern hemispheric insolation [ABSTRACT FROM AUTHOR]