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Double-zero-index properties of electromagnetic and acoustic waveguides have been recently realized based on Dirac/Diraclike cones at the Brillouin zone (BZ) center. However, very limited research has been devoted to double-zero-index structural systems of elastic waveguides, and almost no lattice system has been able to achieve multiple separated Dirac cones generated around different frequencies at the BZ center. Here, we report two separated elastic-wave Dirac-like cones, which are simultaneously achieved around different Dirac points at the BZ center, due to the accidental degeneracy and frequency repulsion effect in a Lieb-like lattice metamaterial. Using the proposed elastic medium, the double-zero-index properties of various elastic wave modes are theoretically analyzed, numerically computed, and experimentally observed at the neighborhood of both Dirac-like points. The performance of near total transmission without the phase change and the ability of wave-front shaping are unambiguously verified by numerical simulation and experimental measurements. Published under license by AIP Publishing.