The paper investigates the effects of uniaxial tensile mechanical strain on the phonon spectra and band structures of monolayer and bilayer molybdenum disulfide (MoS₂) two-dimensional crystals. Using Raman spectroscopy, the authors observe phonon softening and a splitting of the E' Raman mode, extracting a Grüneisen parameter of approximately 1.06. Photoluminescence spectroscopy reveals a linear decrease in the optical band gap of MoS₂, with monolayer MoS₂ showing a reduction of about 45 meV/% strain and bilayer MoS₂ showing a reduction of about 120 meV/% strain. Additionally, a significant decrease in the photoluminescence intensity of monolayer MoS₂ is observed, indicating a direct-to-indirect transition in the optical band gap at a strain of about 1%. These findings demonstrate the first successful strain engineering of the band structure in two-dimensional transition-metal dichalcogenides, opening new avenues for exploring novel physics and tuning optical and electronic properties.The paper investigates the effects of uniaxial tensile mechanical strain on the phonon spectra and band structures of monolayer and bilayer molybdenum disulfide (MoS₂) two-dimensional crystals. Using Raman spectroscopy, the authors observe phonon softening and a splitting of the E' Raman mode, extracting a Grüneisen parameter of approximately 1.06. Photoluminescence spectroscopy reveals a linear decrease in the optical band gap of MoS₂, with monolayer MoS₂ showing a reduction of about 45 meV/% strain and bilayer MoS₂ showing a reduction of about 120 meV/% strain. Additionally, a significant decrease in the photoluminescence intensity of monolayer MoS₂ is observed, indicating a direct-to-indirect transition in the optical band gap at a strain of about 1%. These findings demonstrate the first successful strain engineering of the band structure in two-dimensional transition-metal dichalcogenides, opening new avenues for exploring novel physics and tuning optical and electronic properties.