Exciton-plasmon coupling has recently drawn much interest. In this work, FDTD simulations of exciton-plasmon coupling in plasmonic cavity structures with corrugation patterns are investigated. Excitonic modes are obtained from a Lorentz absorber modeling of a J-aggregate organic dye. The coupling of these excitonic and plasmonic modes on Ag thin films is demonstrated. Rabi splitting due to coupling was clearly observed. Flat metallic surfaces, uniform gratings and Moiré surfaces are used in simulations as corrugation patterns. Metal film thickness and dye concentration dependence of Rabi splitting via exciton-plasmon coupling was also observed on thin flat Ag films. We show that Rabi splitting occurs even at low dye concentrations, and the magnitude of splitting increases as dye concentration increases. A new state in the band gap is observed when the total oscillator strength is increased. Large Rabi splitting is observed when plasmon damping is modulated. Exciton-plasmon coupling on uniform gratings is studied as a function of cavity size, corrugation periodicity and depth. Q factor and Rabi splitting behavior of excitonplasmon coupling on Moiré cavities are investigated as a function of cavity size. Strong anti-crossing is observed when the excitonic absorption matches with the cavity state.