<p>This study establishes a dynamic model for nonlinear metamaterial (NLM) plates with general boundary conditions (BCs) and investigates the nonlinear bandgap behavior. An improved two-dimensional (2D) Fourier series is employed as the admissible function for the transverse displacement of the NLM plate. Using Hamilton's principle, the governing equation for the NLM plate is derived. A semi-analytical expression for the bandgap boundary frequency, dependent on the nonlinear stiffness ratio and vibration amplitude, is developed to predict the nonlinear bandgap of the NLM plate. To explore the mechanism for the bandgap behavior, the nonlinear response of a 2-DOF dynamical system is first studied. The frequency response of the NLM plate is solved using both the harmonic average approach (HAA) and numerical integration. The results are compared to verify the accuracy of the present model. The nonlinear bandgap behavior is further explored from both time-domain and frequency-domain perspectives. The results demonstrate that the steady-state vibration of the NLM plate is reduced by more than 80%. The influences of structural parameters and BCs on the bandgap characteristics are analyzed. The nonlinear bandgap of NLM plates can be optimized by adjusting the structural parameters of nonlinear resonators (NRs). Appropriate structural parameters enable NLM plates to overcome the limitations of traditional linear metamaterial (LM) plates in terms of added mass ratio, achieving low-frequency broadband vibration suppression at lower mass ratios. The theoretical model and analytical study presented in this work provide significant insights for vibration attenuation of NLM plates under general BCs in engineering applications.</p>