The MHD wave is studied when two steep density gradient regions exist
at surfaces of slab plasma. In such a case, it is shown that the surfa
ce Alfven wave has two branches with nearly the same damping rates: si
nce the steep density gradients are located closely each other. Howeve
r, for the sharp boundary plasma, the surface Alfven wave does not dam
p. As the density profile is relaxed, the damping rates become larger,
pass via extremum; and again they become small when the scale length
of the density gradients extremely increases. These damping rates seem
consistent with behavior of magnetic fluctuations observed in the Hel
iotron-E pellet injection experiment.