  The special interest is devoted to such situations when the material space of
our object with affine degrees of freedom has generally lower dimension than
the one of the physical space. In other words when we have the $m$-dimensional
affinely-rigid body moving in the $n$-dimensional physical space, $m<n$. We
mainly concentrate on the physical situation $m=2$, $n=3$ when "thickness" of
flat bodies performs one-dimensional oscillations orthogonal to the
two-dimensional central plane of the body. For the isotropic case in two "flat"
dimensions some special solutions, namely, the stationary ellipses, which are
analogous to the ellipsoidal figures of equilibrium well known in astro- and
geophysics, e.g., in the theory of the Earth's shape, are obtained.
