  Parabolic subalgebras of semi-simple Lie algebras decompose as
$\frak{p}=\frak{m}\oplus\frak{n}$ where $\frak{m}$ is a Levi factor and
$\frak{n}$ the corresponding nilradical. By Richardsons theorem, there exists
an open orbit under the action of the adjoint group $P$ on the nilradical. The
elements of this dense orbits are known as Richardson elements.
  In this paper we describe a normal form for Richardson elements in the
classical case. This generalizes a construction for the general linear group of
Bruestle, Hille, Ringel and Roehrle to the other classical Lie algebra and it
extends the authors normal forms of Richardson elements for nice parabolic
subalgebras of simple Lie algebras to arbitrary parabolic subalgebras of the
classical Lie algebras. As applications we obtain a description of the support
of Richardson elements and we recover the Bala-Carter label of the orbit of
Richardson elements.
