  We compute next-to-next-to-leading order QCD corrections to the gluon-induced
production cross section of Higgs boson pairs in the large top quark mass limit
using the soft-virtual approximation. In the limit of infinitely-heavy top
quark we confirm the results in the literature. We add two more expansion terms
in the inverse top quark mass to the $M_t\to\infty$ result. Since the $1/M_t$
expansion converges poorly, we try to improve on it by factorizing the exact
leading order cross section. We discuss two ways of doing that and conclude
that the finite top quark mass effects shift the cross section at most by about
10\% at next-to-leading order and by about 5\% at next-to-next-to-leading
order.
