In this study, a kind of elastic metamaterial substructure was designed for the selective mode filtering and transmission of symmetric and antisymmetric elastic waves. It is composed of double-sided aluminum-lead composite cylinders arranged in a periodic pattern bounded on an aluminum plate. The band structure of elastic metamaterial unit cell is numerically investigated using the modal analysis of a finite element model (FEM) by treating a unit microstructural cell with the Bloch-Floquet boundary condition. Through analyzing the vibration modes of the unit cell, a complete antisymmetric wave bandgap and a complete symmetric wave bandgap can be formed in different frequency ranges. Considering the geometric complexity of the designed substructure, the dynamic effective mass density of the proposed metamaterial unit cell is calculated by considering the structure as a homogeneous medium under the sub-wavelength requirement. The negative effective mass density behavior for in-plane and out-of-plane plate modes will be presented to verify the bandgap effect of different wave modes. A FEM harmonic analysis is further conducted to obtain the spectral response of a chain model and explore the mode filtering efficiency. Finally, a coupled field transient dynamic FEM is carried out to acquire the dynamic response of the structure. The frequency-wavenumber analysis demonstrates the successful achievement of model filtering behavior. The proposed selective mode transmission control methodology possesses great potential in future SHM and NDE applications. A case study for S0 mode conversion to SH0 mode using a different metamaterial unit cell is exhibited to illustrate other wave control capabilities. The paper finishes with summary, concluding remarks, and suggestions for future work.