Abstract Vibration analysis of periodic multi-span power transmission line systems is conducted and their band-gap characteristics are analyzed. Nonlinear partial differential equations of a unit cell of a periodic multi-span transmission line system are derived using the extended Hamilton principle along with their boundary conditions, where there is rigid-flexible coupling between an insulator and the cable. An accurate global spatial discretization method is used to deal with complex boundary conditions caused by sway of insulators and obtain spatially discretized, linearized equations of the unit cell. Two approaches are used: one spatially discretizes linearized governing partial differential equations and boundary conditions and the other applies Lagrange’s equations to spatially discretized, linearized energy and virtual work expressions. After obtaining spatially discretized, linearized equations, band gaps associated with wave propagation in a periodic infinite-span system are obtained using Bloch theory. Vibration transmissibility and energy distribution of a periodic finite-span system are studied using the transfer matrix method. From the relation between the wave frequency and characteristics of propagation constants, interaction between local vibration of the unit cell and global wave propagation among different spans is illustrated. Band gaps obtained from a finite-span system approach those from an infinite-span system when the number of cells becomes sufficiently large. A comprehensive parametric study is conducted to highlight effects of parameters of insulators and the cable on band gaps of the periodic multi-span transmission line system. Different types of curve veering phenomena that are related to the wave propagation problem of the periodic infinite-span transmission line system are observed for the first time among initial and cut-off frequencies of adjacent band gaps. Existence of band gaps and parametric study results can provide some support for design and vibration control of a power transmission line system.