  The causal structure of the flat brane universe of RSII type is
re-investigated to clarify the boundary conditions for stochastic gravitational
waves. In terms of the Gaussian normal coordinate of the brane, a singularity
of the equation for gravitational waves appears in the bulk. We show that this
singularity corresponds to the ``seam singularity'' which is a singular
subspace on the brane universe. Based upon the causal structure, we discuss the
boundary conditions for gravitational waves in the bulk. Introducing a null
coordinate, we propose a numerical procedure to solve gravitational waves with
appropriate boundary conditions and show some examples of our numerical
results. This procedure could be also applied in scalar type perturbations. The
problem in the choice of the initial condition for gravitational waves is
briefly discussed.
