Abstract: A high-order accurate artificial boundary condition (ABC) for the finite element analysis of near-field wave motion problems is proposed. The out-of-plane wave propagation problem on an unbounded exterior domain is considered. First, an exact dynamic-stiffness ABC that is global in space and time is constructed by solving the initial boundary value problem of a far field using the separation of variables. Second, a temporal localization method that consists of the rational function approximation and the auxiliary variable realization is developed and applied to the dynamic-stiffness ABC, leading to a high-order accurate ABC that is local in time but global in space. Third, the resulting high-order accurate ABC is discretized along the artificial boundary and coupled with the standard lumped-mass finite element equation of a near field. A symmetric second-order system of ordinary differential equations in time is obtained. A new explicit time integration algorithm in structural dynamics is used to solve this system. Finally, numerical examples demonstrate that the proposed ABC is accurate, efficient, stable and easy to implement into the existing finite element codes.