This paper presents a study on strain-induced gap modification in black phosphorus using density functional theory and tight-binding models. The band structure of single-layer black phosphorus and the effect of strain are predicted. The localized orbital composition of the individual bands is determined from first-principles calculations, and the effective low-energy Hamiltonian at the Γ point is derived using the system's symmetry. The results show that deformation in the direction normal to the plane can be used to change the gap size and induce a semiconductor-metal transition. Black phosphorus is a two-dimensional material with a puckered structure, unlike flat graphene. Its structure is composed of flattened P4 clusters, which form a puckered layer. The material has a direct or nearly-direct bandgap and exhibits strong anisotropic dispersion near the gap. The band structure is calculated using first-principles calculations, revealing that the material is a direct bandgap semiconductor with a bandgap of 0.8 eV. The effective low-energy Hamiltonian is constructed based on the symmetry of the material. The Hamiltonian is used to describe the electronic properties of black phosphorus, including the effective masses of the conduction and valence bands. The results show that the bandgap can be modified by applying uniaxial stress perpendicular to the layer, leading to a semiconductor-metal transition. The study also shows that the band structure of black phosphorus changes with compression. The material transitions from a direct bandgap semiconductor to a semimetal and eventually to a metal as the layer is compressed. The bandgap energy decreases with compression, and the conduction band minimum descends below the valence band maximum. The electronic properties of black phosphorus are highly sensitive to strain, making it a promising material for fundamental physics studies. The results demonstrate that black phosphorus can be tuned to exhibit different electronic behaviors by applying strain, highlighting its potential for applications in nanoelectronics and optoelectronics.This paper presents a study on strain-induced gap modification in black phosphorus using density functional theory and tight-binding models. The band structure of single-layer black phosphorus and the effect of strain are predicted. The localized orbital composition of the individual bands is determined from first-principles calculations, and the effective low-energy Hamiltonian at the Γ point is derived using the system's symmetry. The results show that deformation in the direction normal to the plane can be used to change the gap size and induce a semiconductor-metal transition. Black phosphorus is a two-dimensional material with a puckered structure, unlike flat graphene. Its structure is composed of flattened P4 clusters, which form a puckered layer. The material has a direct or nearly-direct bandgap and exhibits strong anisotropic dispersion near the gap. The band structure is calculated using first-principles calculations, revealing that the material is a direct bandgap semiconductor with a bandgap of 0.8 eV. The effective low-energy Hamiltonian is constructed based on the symmetry of the material. The Hamiltonian is used to describe the electronic properties of black phosphorus, including the effective masses of the conduction and valence bands. The results show that the bandgap can be modified by applying uniaxial stress perpendicular to the layer, leading to a semiconductor-metal transition. The study also shows that the band structure of black phosphorus changes with compression. The material transitions from a direct bandgap semiconductor to a semimetal and eventually to a metal as the layer is compressed. The bandgap energy decreases with compression, and the conduction band minimum descends below the valence band maximum. The electronic properties of black phosphorus are highly sensitive to strain, making it a promising material for fundamental physics studies. The results demonstrate that black phosphorus can be tuned to exhibit different electronic behaviors by applying strain, highlighting its potential for applications in nanoelectronics and optoelectronics.