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The effect of material viscoelasticity on the propagation of Lamb wave in a viscoelastic thin plate has been investigated quantitatively. Based on the plane strain theory, a numerical model of the laser-generated Lamb wave is developed in the frequency domain by using the finite element (FE) method. To verify the correctness of the FE model in the frequency domain, a classical FE model in the time domain is established for an elastic plate. The transient waveforms calculated in the frequency domain are in very good agreement with those obtained in the time domain. And then, the laser-generated Lamb waves in the elastic and viscoelastic thin plates are calculated, respectively. By comparing the waveforms of Lamb wave in the two plates, the influence of the material viscoelasticity on the propagation of Lamb waves is studied. Moreover, the effect of the material viscoelastic rate on Lamb waves is analyzed in detail.