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Taking account of the viscoelasticity of materials, the pulsed laser generation of surface acoustic waves in coating–substrate systems has been investigated quantitatively by using the finite element method. The displacement spectra of the surface acoustic waves have been calculated in frequency domain for different coating–substrate systems, in which the viscoelastic properties of the coatings and substrates are considered separately. Meanwhile, the temporal displacement waveforms have been obtained by applying inverse fast Fourier transforms. The numerical results of the normal surface displacements are presented for different configurations: a single plate, a slow coating on a fast substrate, and a fast coating on a slow substrate. The influences of the viscoelastic properties of the coating and the substrate on the attenuation of the surface acoustic waves have been studied. In addition, the influence of the coating thickness on the attenuation of the surface acoustic waves has been also investigated in detail.