Abstract: A fractional-order Maxwell model was used to describe viscoelastic seabed mud.The experimental data of real mud were fitted well by the fractional-order Maxwell model,which had fewer parameters than the traditional one.This model was then applied to investigate the effect of mud on surface-wave damping.The damping rate of a linear monochromatic wave was obtained.The elastic resonance of the mud layer was observed,which led to the peaks of the damping rate.The damping rate was a sum of modal damping rates,which indicated the wave damping induced by mud motions of particular modes.Analysis shows that near resonance,the total damping rate is dominated by the damping rate of the corresponding mode.