Based on density functional theory and density functional perturbation theory calculations, we systematically investigate the vibration responses of monolayer $1H\text{\ensuremath{-}}{\mathrm{MoTe}}_{2}$ to equibiaxial strains. It is found that, at the $\mathrm{\ensuremath{\Gamma}}$ point, the frequency shift of Raman-active modes $({E}^{\ensuremath{'}},$ ${A}_{1}^{\ensuremath{'}},$ and ${E}^{\ensuremath{''}})$ and infrared-active modes $({A}_{2}^{\ensuremath{''}}$ and ${E}^{\ensuremath{'}})$ show domelike shapes; that is, their frequencies decrease monotonically under tensile strains but first increase and then decrease rapidly under compressive strains. The frequency-shift behaviors are revealed to come from vibration responses to both bond stretching and bond-angle bending in strained $1H\text{\ensuremath{-}}{\mathrm{MoTe}}_{2}$. At the $K$ point, a special acoustic mode becomes soft because its frequency drops to zero at a compressive strain of $\ensuremath{-}11.27%$. We find that electron occupancies in Mo ${d}_{{z}^{2}}$, Te ${p}_{x}$, and Te ${p}_{y}$ orbitals weaken the vibration mode at $K$, which exhibits the in-plane vibration of Mo atoms and out-of-plane vibration of Te atoms. On the other hand, compressive strains enhance the Fermi surface nesting and abruptly soften the vibration frequency for one acoustic mode at $K$. Our results point out a way to detect the strain status of monolayer $1H\text{\ensuremath{-}}{\mathrm{MoTe}}_{2}$ by measuring the vibration frequencies.