The band structure of single-layer black phosphorus and the effect of strain are predicted using density functional theory and tight-binding models. Having determined the localized orbital composition of the individual bands from first principles, we use the system symmetry to write down the effective low-energy Hamiltonian at the Γ point. From numerical calculations and arguments based on the crystal structure of the material, we show that the deformation in the direction normal to the plane can be used to change the gap size and induce a semiconductor-metal transition.