Let $R=k[t^{n_1},\dots ,t^{n_s}]=k[x_1,\dots ,x_s]/P$ be a numerical semigroup ring and let $P^{(n)}=P^n{R}_P\cap R$ be the symbolic power of $P$ and $R_s(P)={\oplus }_{i\ge \hspace{0.17em}0}{P}^{(n)}{t}^n$ 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.