Periodic-finite-type shifts (PFTs) form a class of sofic shifts that strictly contains the class of shifts of finite type (SFTs). In this paper, we study PFTs from the viewpoint of certain “periods” that can be associated with them. We define three kinds of periods (descriptive, sequential, and graphical) for PFTs and investigate the relationships between them. The results of our investigation indicate that there are no specific relationships between these periods, except for the fact that the descriptive period of an irreducible PFT always divides its graphical period. Furthermore, we compute the number of periodic sequences in PFTs of a certain type, from which we obtain expressions for their zeta functions.