In order to study stress field of plane and cylindrical waves in viscoelastic medium

the wave motion theories were selected and the stress at the wave front was established. A 3D constitutive model of viscoelastic medium was adopted to describe the dynamic behavior of the medium. The analysis presented herein extended application of wave motion theory in viscoelastic medium. Additionally

the parameter values of viscoelastic boundary were obtained referring to the classical solution in which the behavior of the medium was assumed as linear elastic. The application of the visco-elastic artificial boundary defined by the derivation of this paper was investigated using the finite element program calculated in frequency domain. The results show that high accuracy could be achieved using the artificial boundary established herein

compared with the classical visco-elastic boundary and the viscous boundary which are deduced in elastic medium. As a result of the constitutive model and parameter setting differences between the theoretical analysis in the present paper and the time domain finite element method

a conclusion could be reached that the present results could not be used in the time domain finite element method. Last but not least

a suggestion on further development of the present study has been given

combining the characteristics of time domain finite element method.