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The electron spill-out effect is considered in a singular metasurface. Using the hydrodynamic model, we found that electron spill-out effectively smears the sharp singularity. The introduction of the electron spill-out effect also significantly changes the reflection spectrum, charge distribution, field profile for a singular metasurface. Therefore, this spill-out contribution is crucial and cannot be ignored for a realistic description of optical response in a singular system.