  We study certain family of finite-dimensional modules over the Yangian
$Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal
commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in
the chain $Y(gl_1)\subset Y(gl_2)\subset...\subset Y(gl_N)$. We study the
finite-dimensional $Y(gl_N)$-modules with a semisimple action of the subalgebra
$A(gl_N)$. We call these modules tame.
  We provide a characterization of irreducible tame modules in terms of their
Drinfeld polynomials. We prove that every irreducible tame module splits into a
tensor product of modules corresponding to the skew Young diagrams and some
one-dimensional module.
  The eigenbases of $A(gl_N)$ in irreducible tame modules are called
Gelfand-Zetlin bases. We provide explicit formulas for the action of the
Drinfeld generators of the algebra $Y(gl_N)$ on the vectors of Gelfand-Zetlin
bases.
