In vivo and non-invasive human corneal elasticity measurement is clinically essential, but there is no gold-standard yet. An optical coherence elastography (OCE) method is provided for tissue natural frequency characterization. A microliter (10--40 Pa) air-pulse stimulator is used to induce tissue displacements with the magnitudes ranging from sub-nanometer to micrometer, and a high-resolution optical coherence tomography (OCT) system is used to quantify the resulting tissue dynamics. Both of a temporal relaxation model (R-Model) and a single degree of freedom Voigt model (SDOF-Model) are applied for natural frequency measurements on agar phantoms with concentration (mass fraction) of 1.0%--2.0% as well as on in vivo corneas of two human subjects. The measurement results show that the natural frequency remains the same as the stimulation force is increased from 10 Pa to 40 Pa, and is positively correlated to the square root of Young’s modulus (Pearson’s correlation coefficient is r≥0.98). The SDOF-model is more precise and repeatable. The average coefficients of vitiation (CVs) are only 0.9% for agar phantoms and 1.7% for human corneas using the SDOF-Model, while the average CVs are 8.4% for agar phantoms and 42.6% for human corneas using the R-Model. Compared to the R-Model, the combination of the SDOF-Model with micro-force OCE system is more suitable for in vivo human corneal biomechanics characterization.