In the past decades, many numerical and experimental investigations on the capabilities of periodic structures for vibration attenuation and band localization were performed, and proved those capabilities for different simple structures. Earlier investigation of such phenomenon in periodic plates was not promising due to different factors. A parametric study is a systematic way to vary a number of model parameters and have the system run for one or several analyses for each combination of parameters. In this research, investigation of the effect of varying different parameters on the attenuation bands location and width of four different patterns of periodic plates will be discussed.