Abstract: Based on wave propagating in three directions(x,y,z axis) of elastic foundation,vibrating displacement could be assumed to be in three forms along three directions.Hooke’s law and theory of waves were adopted to deduce the formula of coupled viscous boundary.The coupled viscous boundary could be applied in finite element method.Compared with the theoretical exact solution of Lamb problem,numerical solution could accurately solve the axisymmetric dynamic problems.Although it was deduced in frequency domain,the coupled viscous boundary was independent on frequency.The coupled viscous boundary could be used not only in frequency domain but also in time domain.