In this paper, the generalized analysis and novel application of the multiple pe- riodic (MP) structure are proposed. Both transmission and radiation performances of one di- mensional MP structures are studied. The dispersion relations are analyzed from both layered media (distributive) and lumped circuits aspects. Regarding each aspect, both non-dispersive (conventional) and dispersive (composite right/left-handed (CRLH)) materials are discussed. It is found that with the increase of the periodicity, multiple stopbands are open up due to the re- flections. Meanwhile the space harmonic modes’ separation distance is reduced in the dispersion diagrams. It leads to simultaneously dualistic (right- and left-handed) radiation performance and multi-beam property, and more abundant radiation modes are excited at relatively lower frequencies comparing with conventional periodic structures. A general dispersion relation for- mula and a general Bragg condition for MP structures are derived. The dispersion relation is simply described by the former, and the latter helps to indicate the stopbands locations and engineer the dispersion relation consequently. Applications of MP structures to phase reversal (PR) antennas are also presented in this paper. They experimentally verifies both transmission and radiation characteristics of MP structures. In each analysis, single (SP), double (DP) and triple periodic (TP) structures are presented and compared. This work would also contribute to designs of multi-band devices.