Transition metal dichalcogenides (TMDs) have demonstrated significant potential in nanoelectronics and optoelectronics due to their distinctive electronic, optical and mechanical properties. Strain engineering offers a potent method to tune the bandgap structure and carrier mobility of TMD materials. However, the atomic-scale thickness of these materials poses challenges in applying direct tensile strain. In this study, we utilized a rectangular-shaped blister device combined with in situ micro-Raman spectroscopy to monitor the behaviors of Raman phonon modes in a monolayer MoS₂ sheet during uniaxial extension. We noted phonon softening under strain, which we attributed to the weakening of interatomic bonds in the lattice. This methodology allowed us to determine the Grüneisen parameters of specific Raman modes in monolayer MoS₂, yielding values (${\gamma }_{E_g^2}$=1.35 and ${\gamma }_{A_g^1}$=0.9) that align closely with theoretical predictions. We further tested our methodology on multilayer WSe₂ to confirm its broader applicability.