  Let $\mathcal{E}$ be a set of points in $\mathbb{F}_q^d$. Bennett, Hart,
Iosevich, Pakianathan, and Rudnev (2016) proved that if $|\mathcal{E}|\gg
q^{d-\frac{d-1}{k+1}}$ then $\mathcal{E}$ determines a positive proportion of
all $k$-simplices. In this paper, we give an improvement of this result in the
case when $\mathcal{E}$ is the Cartesian product of sets. More precisely, we
show that if $\mathcal{E}$ is the Cartesian product of sets and
$q^{\frac{kd}{k+1-1/d}}=o(|\mathcal{E}|)$, the number of congruence classes of
$k$-simplices determined by $\mathcal{E}$ is at least
$(1-o(1))q^{\binom{k+1}{2}}$, and in some cases our result is sharp.
