The geomechanical analysis and stability evaluation of reservoir-caprock systems are critical for the successful industrial application of CO2 geological storage. The injection of CO2 into the formation can lead to fluid pressure accumulation, which alters the effective stress field and potentially introduces geological risks. Changes in stress due to CO2 injection could activate faults, induce seismicity, and cause ground motion. In this study, a full 3D field model, incorporating the reservoir, caprock, basement, and surrounding formation, was developed. Given the millions of grid cells within the case model, the computational process necessitates the management of a large volume of data. Utilizing parallel computing, numerical simulations of coupled flow and geomechanics were carried out to analyze the variations in effective stress during CO2 geological storage. The simulation results reveal that during the injection phase, fluid pressure and shear stress incrementally increase over time, while the mean effective stress diminishes. Following the termination of injection, fluid pressure and shear stress decrease but remain elevated compared to the pre-injection equilibrium values. However, the mean effective stress falls below its initial equilibrium value. The augmentation of CPU cores substantially diminishes the computation time of the numerical simulations. However, beyond a certain threshold of cores, the total parallel computation time escalates due to the increased communication burden among processors. As the size of the model being solved enlarges, both the speedup ratio and parallel efficiency increase when using the same number of processors.