  The elementary production cross sections $\pi \Delta \rightarrow Y K$
$(Y=\Sigma,\,\, \Lambda)$ and $\pi N \rightarrow Y K$ are needed to describe
kaon production in heavy ion collisions. The $\pi N \rightarrow Y K$ reactions
were studied previously by a resonance model. The model can explain the
experimental data quite well \cite{tsu}. In this article, the total cross
sections $\pi \Delta \rightarrow Y K$ at intermediate energies (from the kaon
production threshold to3 GeV of $\pi \Delta$ center-of-mass energy) are
calculated for the first time using the same resonance model. The resonances,
$N(1710)\,I(J^P) = \frac{1}{2}(\frac{1}{2}^+)$ and $N(1720)\, \frac{1}{2}
(\frac{3}{2}^+)$ for the $\pi \Delta \rightarrow \Sigma K$ reactions, and
$N(1650)\, \frac{1}{2} (\frac{1}{2}^-)$, $N(1710)\, \frac{1}{2}
(\frac{1}{2}^+)$ and $N(1720)\, \frac{1}{2} (\frac{3}{2}^+)$ for the $\pi
\Delta \rightarrow \Lambda K$ reactions are taken into account coherently as
the intermediate states in the calculations. Also t-channel $K^*(892)
\frac{1}{2}(1^-)$ vector meson exchange is included. The results show that
$K^*(892)$ exchange is neglegible for the $\pi \Delta \rightarrow \Sigma K$
reactions, whereas this meson does not contribute to the $\pi \Delta
\rightarrow \Lambda K$ reactions. Furthemore, the $\pi \Delta \rightarrow Y K$
contributions to kaon production in heavy ion collisions are not only
non-neglegible but also very different from the $\pi N \rightarrow Y K$
reactions. An argument valid for $\pi N \rightarrow Y K$ cannot be extended to
$\pi \Delta \rightarrow Y K$ reactions. Therefore, cross sections for $\pi
\Delta \rightarrow Y K$ including correctly the different isospins must be
