  We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS
representation. We find two classes of trigonometric solutions; diagonal and
non-diagonal. As a lattice model, these two classes of solutions correspond to
RSOS/SOS models with fixed and free boundary spins respectively. Applied to
(1+1)-dimenional quantum field theory, these solutions give the boundary
scattering amplitudes of the particles. For the diagonal solution, we propose
an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix
with boundary and obtain the Bethe ansatz equations.
