Abstract: A method for estimating the viscoelastic parameters of viscoelastic materials according to the experimental data is first constructed. Based on this the Rayleigh normal mode solution have been derived using viscoelastic and elastic theories and separation of variables. The form functions of the double elastic spherical shell with and without viscoelastic material covers are calculated and compared. The echoes are also Presented when short and long pules incident at double elastic spherical shells. The calculations show that the form fullction changes little at low frequencies and reduces more with increasing of frequency. According to analyst the echoes of short pulses, not only the amplitude of the specular renflection but also the amplitude of the surface elastic wave(SEW) reduce.