This paper presents the modeling technique, working mechanism and design guidelines for acoustic multi-stopband metamaterial plates for broadband elastic wave absorption and vibration suppression. The metamaterial plate is designed by integrating two-DOF (degree of freedom) mass-spring subsystems with an isotropic plate to act as vibration absorbers. For an infinite metamaterial plate without damping, a unit cell is modeled using the extended Hamilton’s principle, and two stopbands are obtained by dispersion analysis on the averaged three-DOF model. For a finite metamaterial plate with boundary conditions and damping, shear-deformable conforming plate elements are used to model the whole plate, and stopbands and their dynamic effects are investigated by frequency response analysis and transient analysis by direct numerical integration. Influences of absorbers’ resonant frequencies and damping ratios, plate’s boundary conditions and dimensions, and working plate-absorber modes are thoroughly investigated. Results show that the metamaterial plate is essentially based on the concept of conventional vibration absorbers. The local resonance of the two-DOF subsystems generates two stopbands, and the inertial forces generated by the resonant vibrations of absorbers straighten the plate and attenuate/stop wave propagation. Each stopband’s bandwidth can be increased by increasing the absorber mass and/or reducing the isotropic plate’s unit cell mass. Moreover, a high damping ratio for the secondary absorber can combine the two stopbands into one wide stopband for vibration suppression, and a low damping ratio for the primary absorber warrants absorbers’ quick response to steady and/or transient excitations.