In this work, we predicted three new two-dimensional (2D) Be 2 C structures, namely, α-Be 2 C, β-Be 2 C, and γ-Be 2 C, on the basis of density functional theory (DFT) computations and the particle-swarm optimization (PSO) method. In α-Be 2 C, a carbon atom binds to eight Be atoms, forming an octacoordinate carbon moiety. This is the first example of an octacoordinate carbon containing material. The other two structures, β-Be 2 C and γ-Be 2 C, are quasi planar hexacoordinate carbon (phC) containing 2D materials. Good stability with these three phases is revealed by their lower cohesive energy and positive phonon modes. More interestingly, these predicted new phases of Be 2 C are all semiconductors and have unusual negative Poisson's ratios (NPRs). If synthesized, 2D Be 2 C materials will have a broad range of applications in electronics and mechanics.