The proposed numerical design approach investigates both infinite and finite models and includes an experimental validation of elastic wave absorption and vibration suppression for flexural wave band gaps in metamaterial plates. The resonant metamaterial is obtained using a 2-dimensional periodic array of resonators (mass-screws) mounted to a thin homogeneous plate. The sensitivity analysis of the band gap frequency range takes into account the uncertainties of all the design parameters of the metamaterial plate. The theoretical approach uses the finite element method (FEM) to compare the predicted band gaps, which are derived from infinite and finite models of the metamaterial. An automatic method is proposed to detect the frequency ranges of band gaps in the finite metamaterial based on the behavior of the corresponding bare plate. Directional plane wave excitation and point force excitation are applied to evaluate the efficiency of the detection method. The results of these analyses are compared with experimental measurements. The frequency ranges of experimental vibration attenuation are in good agreement with the theoretically predicted complete and directional band gaps.