  Elastic constants and sound velocities of nm-order thin films are essential
for designing acoustic filters. However, it is difficult to measure them for
dielectric thin films. In this study, we use a three-layer structure where a
dielectric nano-thin film is sandwiched between thicker metallic films to
measure the longitudinal elastic constant of the dielectric film. We propose an
efficiency function to estimate the optimal thicknesses of the components. We
use Pt/NiO/Pt three-layer films for confirming our proposed method. The
determined elastic constant of NiO deposited at room temperature is smaller
than the bulk value by $\sim$40$\%$. However, it approaches the bulk value as
the deposition temperature increases. We also reveal that uncertainty of the
elastic constant of the Pt film insignificantly affects the accuracy of the
determined elastic constant of NiO in this structure.
