  I construct a correspondence between the Schubert cycles on the variety of
complete flags in C^n and some faces of the Gelfand-Zetlin polytope associated
with the irreducible representation of SL_n(C) with a strictly dominant highest
weight. The construction is based on a geometric presentation of Schubert cells
by Bernstein-Gelfand-Gelfand using Demazure modules. The correspondence between
the Schubert cycles and faces is then used to interpret the classical Chevalley
formula in Schubert calculus in terms of the Gelfand-Zetlin polytopes. The
whole picture resembles the picture for toric varieties and their polytopes.
