A metal plate array (MPA) is the complementary structure of a metal hole array and forms spoof surface plasmon polaritons (SSPPs) supported by parallel plate modes in a unit cell. A ring dipole array, which is a periodic structure designed by providing an aperture in the conductive part of the unit cell of an MPA, has the potential to produce bound states in the continuum (BICs). In this paper, the transformation from SSPPs to BICs is confirmed using these two structures by broadening the aperture in the unit cell. Making use of this phenomenon, control of the skin depth of surface modes is numerically demonstrated while retaining the resonant frequency, and the fitting values of the plasmonic skin depth are in good agreement with theoretical values.