In 2000, Rees and Shalaby constructed simple, indecomposable two-fold cyclic triple systems for all $v\equiv 0,1,3,4,7$ and $9~ (\textup{mod}~12)$, where $v=4$ or $v\geq 12$, using Skolem-type sequences.
We construct three-fold triple systems having the properties of being cyclic, simple and indecomposable for all admissible orders, using Skolem-type sequences.