Based on the theory of plane strain and the elastic equations of dynamic equilibrium,the equations of dynamic equilibrium in the frequency domain are derived. The finite element models of laser-generated Lamb waves in the time and frequency domain are established for elastic material. Based on the numerical calculations,the solving process of the two models is compared. Moreover,the characteristics of laser-generated Lamb waves on a thin viscoelastic plate are analyzed in the frequency domain. The results show laser-generated Lamb waves mainly include the lower frequency components of the weak dispersion symmetric mode and the dispersive anti-symmetric mode. The propagation of laser-generated Lamb waves on viscoelastic materials can be calculated effectively by the finite element model in the frequency domain. In addition,the amplitudes of Lamb waves are attenuated in the viscoelastic material,and the attenuation coefficients to different modes of the wave are different.