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Injection of CO2 for geologic carbon sequestration into deep sedimentary formations involves fluid pressure increases that engage hydromechanical processes that can cause seismicity by activation of existing faults. In this work, we use a coupled multiphase fluid flow and geomechanical simulator to model spatiotemporal fluid pressure and stress changes in order to study the poroelastic effect of CO2 injection on faults in crystalline basement rock below the injection zone. The seismicity rate along features interpreted to be basement faults is modeled using Dieterich's rate‐and‐state earthquake nucleation model. The methodology is applied to microseismicity detected during CO2 injection into the Mount Simon formation during the Illinois Basin—Decatur Project. The modeling accurately captures an observed reduction in seismicity rate when the injection in the second well was into a slightly shallower zone above the base of the Mount Simon formation. Moreover, the modeling shows that it is important to consider poroelastic stress changes, in addition to fluid pressure changes for accurately modeling of the observed seismicity rate. Plain Language Summary: The Illinois Basin—Decatur Project (IBDP) is the first carbon capture and sequestration project in the United States to inject commercial volumes of CO2 into underground subsurface rock formations. Nearly 20,000 injection‐induced microearthquakes have been detected during the 3 year‐long injection, mainly located within the basement rock beneath the reservoir where the CO2 is injected. In this work, we aim to model the sequence of microearthquakes induced by the injection of CO2 into a permeable reservoir above a crystalline basement rock using a computational model that couples fluid flow and geomechanics. Changes in in situ conditions are linked to seismicity induced at the site using an earthquake physics‐based model. Our model correctly reproduces the main temporal features of the earthquake sequence observed at the IBDP. Key Points: We model CO2 injection in a Mount Simon sandstone reservoir above crystalline basement faultsWe model injection‐induced seismicity using a rate‐and‐state earthquake nucleation modelSeismicity induced at the Illinois Basin—Decatur Project is mainly pressure‐driven but poroelastic effects are not negligible [ABSTRACT FROM AUTHOR]