  We present the numbers of ice model and eight-vertex model configurations
(with Boltzmann factors equal to one), I(n) and E(n) respectively, on the
two-dimensional Sierpinski gasket SG(n) at stage $n$. For the eight-vertex
model, the number of configurations is $E(n)=2^{3(3^n+1)/2}$ and the entropy
per site, defined as $\lim_{v \to \infty} \ln E(n)/v$ where $v$ is the number
of vertices on SG(n), is exactly equal to $\ln 2$. For the ice model, the upper
and lower bounds for the entropy per site $\lim_{v \to \infty} \ln I(n)/v$ are
derived in terms of the results at a certain stage. As the difference between
these bounds converges quickly to zero as the calculated stage increases, the
numerical value of the entropy can be evaluated with more than a hundred
significant figures accurate. The corresponding result of ice model on the
generalized two-dimensional Sierpinski gasket SG_b(n) with $b=3$ is also
obtained. For the generalized vertex model on SG_3(n), the number of
configurations is $2^{(8 \times 6^n +7)/5}$ and the entropy per site is equal
to $\frac87 \ln 2$. The general upper and lower bounds for the entropy per site
for arbitrary $b$ are conjectured.
