We predict two-dimensional Be materials, α- and β-beryllene. In α-beryllene each Be atom binds to six other Be atoms in a planar scheme, whereas β-beryllene consists of two stacked α-beryllene monolayers. Both α- and β-beryllene are found to be highly stable, as demonstrated by high cohesive energies close to that of bulk Be, an absence of imaginary phonon modes, and high melting points. Both materials are metallic, indicating potential applications in Na-ion and K-ion batteries, which are explored in detail. The diffusion barriers of Na (K) on α- and β-beryllene are found to be only 9 (3) and 4 (5) meV, respectively. In particular, the diffusion barrier of K on α-beryllene exhibits the lowest ever recorded value in two-dimensional materials, suggesting the possibility of ultrafast charge/discharge. As the theoretical specific capacities of Na/K on α- and β-beryllene are found to be 1487/1322 and 743/743 mA h g–1, respectively, the storage capacity is ultrahigh.