  We give a detailed analysis of long range cumulative scattering effects from
rough boundaries in waveguides. We assume small random fluctuations of the
boundaries and obtain a quantitative statistical description of the wave field.
The method of solution is based on coordinate changes that straighten the
boundaries. The resulting problem is similar from the mathematical point of
view to that of wave propagation in random waveguides with interior
inhomogeneities. We quantify the net effect of scattering at the random
boundaries and show how it differs from that of scattering by internal
inhomogeneities.
