  In this paper, we consider polyhedral realizations for crystal bases
$B(\lambda)$ of irreducible integrable highest weight modules of a quantized
enveloping algebra $U_q(\mathfrak{g})$, where $\mathfrak{g}$ is a classical
affine Lie algebra of type ${\rm A}^{(1)}_{n-1}$, ${\rm C}^{(1)}_{n-1}$, ${\rm
A}^{(2)}_{2n-2}$ or ${\rm D}^{(2)}_{n}$. We will give explicit forms of
polyhedral realizations in terms of extended Young diagrams or Young walls that
appear in the representation theory of quantized enveloping algebras of
classical affine type. As an application, a combinatorial description of
$\varepsilon_k^*$ functions on $B(\infty)$ will be given.
