  We consider the growth of density perturbations in the presence of
self--interacting dark matter, SIDM, proposed by Carlson, Machacek and Hall
(1992). We determine the range of values for the coupling constant $\lambda$
and the particle mass $m^\prime$, for which the power spectrum lies in the
``allowed" range based on constraints from the IRAS galaxy survey and damped
Lyman--$\alpha $ systems. Our results show that no combination of parameters
can meet both limits. We consider constraints on the $\2-2$ scatterings which
keep the SIDM particles in pressure equilibrium, and we show that if such
interactions maintain pressure equilibrium down to the present, they will be
strong enough to disrupt galaxy mergers and may lead to stripping of galaxy
halos as galaxies move through the dark matter background of these particles.
Hence, we also investigate the evolution of large-scale structure in the SIDM
model when the particles drop out of pressure equilibrium at some higher
redshift. The resulting free-streaming leads to an additional suppression of
small-scale perturbations, but it does not significantly affect our results.
