This study proposes EMMs made of molded pulp and steel composite structures; molded pulp can be used to manufacture periodic shapes with low cost and environmental burden, which can help in the application of EMMs to steel structures that are widely used in engineering products. Toward this end, the frequency-dependent mechanical properties of the molded pulp are first identified via the vibration testing of pulp-steel laminate structures; the measured data confirm the high damping properties of molded pulp. Subsequently, wave propagation within the EMM is analyzed using the wave finite element method via dispersion curves, which suggest that the EMMs fabricated using molded pulp can attenuate wave propagation in wide frequency ranges by combining the effects of geometrical periodicity (i.e., band gap) and the material damping of the molded pulp. Further, the effects of geometrical parameters on band gaps are investigated; the results indicate that the proposed EMMs can open up band gaps in frequency ranges lower than 1000 Hz for thin plates used in engineering products. Finally, the frequency response functions of the EMMs are experimentally measured; the results confirm that EMMs can suppress vibrations in wide frequency ranges corresponding to the wave attenuation obtained by the dispersion analysis.