  It is well known that the Einstein equation on a Riemannian flag manifold
$(G/K,g)$ reduces to a algebraic system, if $g$ is a $G$-invariant metric. In
this paper we described this system for all flag manifolds of a classical Lie
group. We also determined the number of isotropy summands for all of these
spaces and proved certain properties of the set of t-roots for flag manifolds
of type $B_n$, $C_n$ and $D_n$.
