Abstract: The concept of the consistent viscous-spring artificial boundaries and viscous-spring boundary elements was proposed.The stiffness matrix and damp matrix of the 2D consistent artificial boundaries were deduced.The equivalent viscous-spring artificial boundary elements were developed by comparing the matrix of the general finite element and the consistent viscous-spring artificial boundaries.This method was applied to the uniform and layered half space problems.It was shown that the precision of viscous-spring boundary elements was the same as that of lumped viscous-spring artificial boundaries.The viscous-spring boundary elements were efficient and could be applied simply.