  The eikonal approximation (EA) is widely used in various high-energy
scattering problems. In this work we generalize this approximation from the
scattering problems with time-independent Hamiltonian to the ones with
periodical Hamiltonians, {\it i.e.}, the Floquet scattering problems. We
further illustrate the applicability of our generalized EA via the scattering
problem with respect to a shaking spherical square-well potential,
  by comparing the results given by this approximation and the exact ones. The
generalized EA we developed is helpful for the research of manipulation of
high-energy scattering processes with external field, {\it e.g.}, the
manipulation of atom, molecule or nuclear collisions or reactions via strong
laser fields.
