  Every Steiner triple system is a uniform hypergraph. The coloring of
hypergraph and its special case Steiner triple systems, {STS}$(v)$, is studied
extensively. But the defining set of the coloring of hypergraph even its
special case {STS}$(v)$, is not explored yet. We study minimum defining set and
the largest minimal defining set for $3$-coloring of {STS}$(v)$. We determined
minimum defining set and the largest minimal defining set, for all
non-isomorphic {STS}$(v)$, $v\le 15$. Also we have found the {\sf defining
number} for all Steiner triple systems of order $v$, and some lower bounds for
the size of the largest minimal defining set for all Steiner triple systems of
order $v$, for each admissible $v$.
