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In recent years, there has been a growing recognition that the rocking motion of structures, especially cylindrical ones, should be evaluated with three‐dimensional (3D) models. However, dissipation mechanisms in 3D models are complex and have yet to be well established. This paper presents an analytical study on an inherent dissipation mechanism based on the rolling friction model and an external dissipation mechanism based on energy dissipators (EDs) for 3D rocking cylindrical structures. Through a variational formulation, the nonlinear equations of motion are derived considering the rolling friction model and the Bouc–Wen model. Compared with the existing inherent dissipation model in literature, the rolling friction model has a noticeable advantage that it can capture the energy dissipation behavior during free vibration under various initial conditions. Additionally, the rolling friction model is more versatile since the contact coefficient is adjustable. On the other hand, external EDs further enhance the energy dissipation of the structures. Roles of the inherent and external mechanisms in the 3D rocking motion of cylindrical structures against earthquakes are assessed using a series of near‐fault pulse‐like ground motions. Results indicate the inherent dissipation mechanism, that is, the rolling friction model, cannot avoid overturning under near‐fault pulse‐like ground motions, leading to unstable structures. This is because an uplifted cylinder will continuously absorb energy from earthquake excitations, while the amount of energy dissipated by the rolling friction model is small. Comparatively, adding external EDs is effective in mitigating seismic responses and thereby avoiding overturning.

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