  We give a general construction for finite dimensional representations of
$U_q(\hat{\G})$ where $\hat{\G}$ is a non-twisted affine Kac-Moody algebra with
no derivation and zero central charge. At $q=1$ this is trivial because
$U(\hat{\G})=U({\G})\otimes \C(x,x^{-1})$ with $\G$ a finite dimensional Lie
algebra. But this fact no longer holds after quantum deformation. In most cases
it is necessary to take the direct sum of several irreducible
$U_q({\G})$-modules to form an irreducible $U_q(\hat{\G})$-module which becomes
reducible at $q = 1$. We illustrate our technique by working out explicit
examples for $\hat{\G}=\hat{C}_2$ and $\hat{\G}=\hat{G}_2$. These finite
dimensional modules determine the multiplet structure of solitons in affine
Toda theory.
