The realization of artificial boundary condition and wave input are the key factors for the numerical simulation of wave scattering in semi-infinite domain. To determine the wave input, the one-dimensional or two-dimensional free-field problems have been analyzed for vertically-incident plane waves or obliquely-incident waves in the direction parallel to the plane of the two axes, which, however, cannot account for an incident wave in an arbitrary direction in the three-dimensional problems and limits the applications. A feasible method to solve the input of an incident plane seismic wave in an arbitrary direction is proposed in this paper. First, the two-dimensional free-field problem is analyzed through the Thomson-Haskell transfer matrix method. Then, the three-dimensional free-field motion is obtained through the transformation between two coordinate systems. Combined with the lumped-mass explicit finite element method (FEM), the input for transmitting boundary and viscous-spring artificial boundary are realized. The method is verified and the effect of incident angle is demonstrated through numerical examples.