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New ternary zinc oxyfluorotellurite (ZOFT) with the composition (ZnO)x-(AlF3)y-(TeO2)z, where 5≤x<35; 5≤y≤25; 60≤z≤70, has been successfully prepared by the conventional rapid melt quenching technique. Density, molar volume, and glass transition temperature have been assessed for each ZOFT glass sample. The longitudinal and transverse ultrasonic waves propagated in each glass sample were measured using a MBS8020 ultrasonic data acquisition system at 5 MHz frequency and room temperature. The longitudinal modulus (L), shear modulus (G), Young’s modulus (E), bulk modulus (K), and Poisson’s ratio (σ) are assessed from both velocity data and their respective density. The compositional dependence of the ultrasonic velocities and related parameters are discussed to understand the rigidity and compactness of the glass system studied.