  We discuss a locally supersymmetric formulation for the boundary
Fayet-Iliopoulos (FI) terms in 5-dimensional U(1) gauge theory on $S^1/Z_2$,
using the four-form multiplier mechanism to introduce the necessary $Z_2$-odd
FI coefficient. The physical consequence of the boundary FI terms is studied
within the full supergravity framework. For both models giving a flat and a
warped spacetime geometry, the only meaningful deformation of vacuum
configuration induced by the FI terms is a kink-type vacuum expectation value
of the vector multiplet scalar field which generate a 5D kink mass for charged
hypermultiplet. This result for the four-form induced boundary FI terms is
consistent with the one derived by the superfield formulation of 5D conformal
supergravity.
