Elastic edge states, formed by interfacing different topological phases and appealing for various cutting-edge applications based on surface acoustic waves, often exhibit limits due to the lack of strong topological protection. Here, we overcome this difficulty by engineering a synthetic three-dimensional (3D) Dirac semimetal phase in a 2D elastic metamaterial. By tuning a geometry parameter, we drive topological transitions, which can be mapped into Dirac points in hybrid 3D, i.e., 2D plus a synthetic dimension. Gapless adiabatic spectral flows are found along the synthetic momentum loops when they encircle the Dirac points, emerging as the surface-arc states in hybrid 3D, that restores the bulk-edge correspondence in elastic systems. Experimental measurements confirm the bulk Dirac points, surface-arc states linking oppositely charged Dirac points, and the emergent gapless spectral flows. This Letter brings novel quantum-inspired phenomena to elastic systems and may inspire applications in topological control of mechanical waves and dynamics.

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• Geometric & topological phases
• Mechanical metamaterials
• Metamaterials
• Topological materials