  In this work, we provide a way to completely determine the set of pure gaps
$G_0(P_1, P_2)$ at two rational places $P_1, P_2$ in a function field $F$ over
a finite field $\mathbb{F}_q$, and its cardinality. Furthermore, we given a
bound for the cardinality of the set $G_0(P_1, P_2)$ which is better, in some
cases, than the generic bound given by Homma and Kim. As a consequence, we
completely determine the set of pure gaps and its cardinality for two families
of function fields: the $GK$ function field and Kummer extensions.
