Let $R=k[t^{n_{1}},\ldots ,t^{n_{s}}]=k[x_{1},\ldots ,x_{s}]/P$ be a numerical semigroup ring and let $P^{(n)} = P^nR_P \cap R$ be the symbolic power of $P$ and $R_s(P) = \oplus_{i\geq 0}P^{(n)}t^n$ the symbolic Rees ring of $P$. It is hard to determine symbolic powers of $P$; there are even non-Noetherian symbolic Rees rings for 3-generated semigroups. We determine the primary decomposition of powers of $P$ for some classes of 3-generated numerical semigroups.