  For a positive integer $m$, a finite set of integers is said to be evenly
distributed modulo $m$ if the set contains an equal number of elements in each
congruence class modulo $m$. In this paper, we consider the problem of
determining when the set of gaps of a numerical semigroup $S$ is evenly
distributed modulo $m$. Of particular interest is the case when the nonzero
elements of an Ap\'ery set of $S$ form an arithmetic sequence, which occurs
precisely when $S$ is a numerical semigroup of embedding dimension 2 or a
numerical semigroup of maximal embedding dimension generated by a generalized
arithmetic sequence. We derive explicit conditions for which the gaps of these
numerical semigroups are evenly distributed modulo $m$.
