We demonstrate the use of phase-stabilized swept-source optical coherence tomography to assess the propagation of low-amplitude (micron-level) waves induced by a focused air-pulse system in tissue-mimicking phantoms, a contact lens, a silicone eye model, and the mouse cornea in vivo. The results show that the wave velocity can be quantified from the analysis of wave propagation, thereby enabling the estimation of the sample elasticity using the model of surface wave propagation for the tissue-mimicking phantoms. This noninvasive, noncontact measurement technique involves low-force methods of tissue excitation that can be potentially used to assess the biomechanical properties of ocular and other delicate tissues in vivo.