  We investigate here a supermatrix model with a mass term and a cubic
interaction. It is based on the super Lie algebra osp(1|32,R), which could play
a role in the construction of the eleven-dimensional M-theory. This model
contains a massive version of the IIB matrix model, where some fields have a
tachyonic mass term. Therefore, the trivial vacuum of this theory is unstable.
However, this model possesses several classical solutions where these fields
build noncommutative curved spaces and these solutions are shown to be
energetically more favorable than the trivial vacuum. In particular, we
describe in details two cases, the SO(3) \times SO(3) \times SO(3) (three fuzzy
2-spheres) and the SO(9) (fuzzy 8-sphere) classical backgrounds.
