  In this paper, we develop a finite field analogue for one of the Lauricella
series, $F^{(n)}_A$. Extending results of Greene, a finite field analog for the
multinomial coefficient is developed in order to express the Lauricella series
in terms of binomial coefficients. We have further deduced certain
transformation and reduction formulas for the Lauricella series $F^{(n)}_A$.
Finally, we have obtained a number of generating functions for the Lauricella
series $F^{(n)}_A$.
