Optical properties of two-dimensional periodic annular cavity arrays in hexagonal packing are investigated by finite difference time domain simulation method in this paper. According to simulated reflectance/transmission spectra, electric field distribution and charge distribution, we confirm that multiple cylindrical surface plasmon resonances, which result in reflectance dips, can be excited in annular cavities by linearly polarized light. Mechanism of the cylindrical surface plasmons is investigated. A coaxial waveguide mode TE11 is excited in the annular cavities and a Fabry-Perot resonance is fulfilled along the depth direction of the annular cavities at the resonance wavelengths. While the number of reflectance dips and wavelengths of these dips in reflectance spectra are dependent on the geometric sizes of the annular cavities, the periodicity and polarization of incident light do not affect their reflectance spectra dramatically. Incident light beams with resonant wavelengths are localized in annular cavities with large electric field increasing and dissipate gradually due to metal loss. Reflectance dips can be tuned from 350 to 2000 nm by adjusting geometric size parameters of the annular cavities, such as outer and inner radii of the annular gaps, gap sizes and metal film thickness values. Reflectance dips shift toward longer wavelength with increasing inner and outer radii of the annular gaps, metal film thickness and with reducing the gap distance. In addition, infiltrate liquids in the annular gaps will result in a shift of the resonance wavelengths, which makes the annular cavities good refractive index sensors. A refractive index sensitivity up to 1850 nm/RIU is demonstrated. The refractive index sensitivities of annular cavities can also be tuned by their geometric sizes. Annular cavities with large electric field enhancement and tunable cylindrical surface plasmons can be used as surface enhanced Raman spectra substrates, refractive index sensors, nano-lasers and optical trappers.