  We introduce fusion $U_q(G^{(1)}_2)$ vertex models related to fundamental
representations. The eigenvalues of their row to row transfer matrices are
derived through analytic Bethe ans{\"a}tze. By combining these results with our
previous studies on functional relations among transfer matrices(the
$T$-system), we conjecture explicit eigenvalues for a wide class of fusion
models. These results can be neatly expressed in terms of a Yangian analogue of
the Young tableaux.
