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We report investigations on the elasticity of superconducting FeSe using picosecond ultrasonic technique. The tetragonal (001) FeSe thin film, deposited on a processed SrTiO3 substrate by the pulsed laser deposition, exhibits distinct c-axis preferred orientation and single-crystalline features as a result of the x-ray diffraction. The high-quality crystallinity thus enables quantitative examinations of anisotropic stiffness coefficients (C33) of FeSe, correlating to the interatomic interaction in the simplest iron-based superconductor. Our experiment indicates a room-temperature C33 of 40.9 ± 0.4 GPa and material stiffening of 4.3% at low temperatures, which can be explained by the weakening of anharmonic phonon-phonon interactions. [ABSTRACT FROM AUTHOR]