  A model of representations of a Lie algebra is a representation which a
direct sum of all irreducible finite dimensional representations taken with
multiplicity $1$. In the paper an explicit construction of a model of
representation for all series of classical Lie algebras is given. The
construction does not differ much for different series. The space of the model
is constructed as a space of polynomial solutions of a system of partial
differential equations. The equations in this system are constructed form
relations between minors of matrices from the corresponding Lie group. This
system has a simplification which is very close to the GKZ system, that is
satisfied by $A$-hypergeometric functions.
