We investigate the complex band structure and forced response of flexural waves propagating in an elastic metamaterial thick plate. Mindlin-Reissner thick plate theory is considered. We study the influence of periodic arrays of spring-mass resonators attached to the surface of a homogeneous thick plate on the formation of Bragg-type and locally resonant band gaps. The plane wave expansion and extended plane wave expansion approaches are used to compute the complex band structure and wave shapes of the metamaterial thick plate with attached spring-mass resonators. An experimental analysis is conducted with a 3D-printed metamaterial plate with resonators. Modal shapes, forced response and band structure are computed by finite element and wave finite element methods. Analytical, numerical and experimental results present good agreement.