An electromagnetic cavity resonator with deep subwavelength size is considered theoretically on plasmonic nanowires with periodically modulated permittivity. In this work, plasmonic nanowires are treated as ∈-negative cylindrical waveguides (ENGCWs) in a certain band of frequency whose guided wavelength for a small radius waveguide is small compared to the free-space wavelength. The dispersion relations of an ENGCW with permittivity varied periodically along the axial direction are then studied analytically using the space harmonic method and evanescent modes near the center of the band gap are analyzed in detail. By properly creating a "defect" on such a periodically modulated (PM) ENGCW, a cavity on this nanowire can be synthesized whose dimension along the wire is determined by the guided wavelength and the decay rate of the evanescent mode, resulting in an ultracompact subwavelength cavity resonator with a size much smaller than the free-space wavelength. The effective size of this cavity is calculated numerically. The finite-element method (FEM) is used to simulate the reflection phenomena at the interface of ENGCW/PMENGCW and to demonstrate the cavity mode. The quality factor (Q) is discussed and calculated from the FEM results. Candidate materials suitable for making this structure are suggested. A method to realize such a resonating structure using only one material is also briefly analyzed. Finally, a few words about the lower limit of such nanowires are given.