Edge states in lattices typically rely on defects, topology, or parameter tuning, and occupy narrow spectral windows. Here, we demonstrate an edge-dominated mechanism driven by the Poincaré conformal metric. By projecting the hyperbolic metric onto elastic trusses, we show that the spatially varying bar lengths naturally embed the metric into the structural dynamic properties. This spatial modulation of the local dynamic scale inherently drives higher-index eigenmodes toward the boundary, yielding an accumulation of edge states. Furthermore, conformal mapping extends this mechanism to arbitrary boundaries, enabling the design of interconnected boundary-channel networks. Transient wave propagation confirms boundary-guided transport, establishing a topology-free route for programmable wave localization and energy focusing in mechanical metamaterials.

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• Edge states
• Mechanical metamaterials
• Symmetry protected topological states
• Hyperbolic lattice