In this paper, flexural wave propagation, attenuation, and reflection through finite number of rigid elastic combined metabeam (RECM) elements sandwiched between two Euler Bernoulli beams has been studied, implementing the spectral element, inverse Fourier transform, and transfer matrix method. Spectral element has been formulated for the unit representative cell of RECM employing the rigid body dynamics. Governing dimensionless parameters are identified. Furthermore, the sensitivity analysis has been carried out to comprehend the influence of non-dimensional parameters, such as mass ratio, length ratio, and rotary inertia ratio on the attenuation profile. Rotary inertia of rigid body produces local resonance (LR) band, which may abridge the gap between the two Bragg scattering (BS) bands and results in an ultra-wide stop band for the specific combination of governing non-dimensional parameters. A total of 164% normalized attenuation band is possible to obtain in RECM. Natural frequencies for the finite RECM have also been evaluated from the global spectral element matrix and observed that some natural frequencies lie in the attenuation band. Therefore, the level of attenuation near that natural frequencies is significantly less and cannot be identified from the dispersion diagram of the infinite RECM.