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Understanding dynamic stability of a ship at a resonance frequency is important because comparatively smaller external forces and moments generate larger motions. The roll motion is most susceptible because of smaller restoring moments. Most studies related to the failure modes such as parametric roll and dead ship condition, identified by second generation of intact stability criteria (SGISC) are performed at a resonance frequency. However, the nature of resonance, where the model experiences an incremental roll motion, has not been well understood. In this study, nonlinear unsteady computational fluid dynamics (CFD) simulations were conducted to investigate the resonance phenomenon using a containership under a sinusoidal roll exciting moment. To capture the complexity of the phenomenon, simulations were conducted over a range of frequencies to cover the resonance frequency including lower and higher amplitudes. In addition to the resonance frequency, the phase shift between roll exciting moment and roll angle, as well as the phase difference between acceleration and roll angle, were found to have significant effects on the occurrence of resonance.