Abstract: The interaction of fast charged particles with graphene layers can generate electromagnetic modes. This wake effect has been recently proposed for short-wavelength, high-gradient particle acceleration and for obtaining brilliant radiation sources. In this study, the excitation of wakefields produced by a point-like charged particle moving parallel to a multilayer graphene array (which may be supported by an insulated substrate) is studied using the linearized hydrodynamic theory. General expressions for the excited longitudinal and transverse wakefields have been derived. The dependencies of the wakefields on the positions of the layers and the substrate, the velocity and the surface density have been extensively analyzed. This study provides a deeper understanding of the physical phenomena underlying plasmonic excitations in graphene layers, paving the way for potential applications of these structures in particle acceleration, nanotechnology and materials science.