We investigate the mechanical and vibrational properties of three quasiplanar two-dimensional (2D) monolayers (${\mathrm{Be}}_2\mathrm{C}, {\mathrm{Be}}_5{\mathrm{C}}_2$, and ${\mathrm{B}}_4{\mathrm{C}}_3$) containing hypercoordinate carbon centers. Density functional theory was employed to determine the elastic response, Young's modulus, Poisson's ratio, and dynamical stability. ${\mathrm{B}}_4{\mathrm{C}}_3$ exhibits the highest in-plane stiffness ($\sim 249\mathrm{N}/\mathrm{m}$), nearly isotropic elasticity, and large cohesive energy, consistent with high mechanical resilience. ${\mathrm{Be}}_5{\mathrm{C}}_2$ displays strong elastic anisotropy and a negative Poisson's ratio ($\nu =-0.36$), indicative of auxetic behavior. ${\mathrm{Be}}_2\mathrm{C}$ shows intermediate stiffness and moderate flexibility. Phonon dispersions confirm that all three monolayers are dynamically stable. Electron localization function and crystal orbital Hamilton population analyses reveal extensive multicenter σ networks complemented by modest π delocalization ($\sim 10–15\%$), which facilitates uniform stress redistribution under deformation. These findings connect the topology of multicenter bonding with macroscopic elastic response, offering design guidelines for lightweight and flexible 2D materials.

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• Chemical bonding
• Mechanical deformation
• Phonons
• Poisson ratio
• Carbides
• Monolayer films
• Density functional calculations