  We consider the gravitational model with additional spatial dimensions and
anisotropic pressure which is nonzero only in these dimensions. Cosmological
solutions in this model include accelerated expansion of the Universe at late
age of its evolution and dynamical compactification of extra dimensions. This
model describes observational data for Type Ia supernovae on the level or
better than the $\Lambda$CDM model. We analyze two equations of state resulting
in different predictions for further evolution, but in both variants the
acceleration epoch is finite.
