Optical coherence tomography (OCT) provides high spatial resolution and sensitivity that are ideal for imaging the cornea and lens. Quantifying the biomechanical properties of these tissues could add clinically valuable information. Thus, we propose a dynamic elastography method combining OCT detection and a mechanical actuator to map the shear modulus of soft tissues. We used a piezoelectric actuator driven in the kHz range and we used phase-sensitive OCT (PhS-OCT) to track the resulting shear waves at an equivalent frame rate of 47 kHz. We mapped the shear wave speed of anesthetized mice cornea using monochromatic excitations. We found a significant difference between a group of knock-out (3.92 ± 0.35 m/s, N=4) and wild-type mice (5.04 ± 0.51 m/s, N=3). These preliminary results demonstrate the feasibility of using PhS-OCT to perform in vivo shear wave elastography of the cornea. We then implemented a shear pulse compression approach on ex vivo human cornea. For that purpose, frequency- modulated excitations were used and the resulting displacement field was digitally compressed in a short broadband pulse with a 7 dB gain in signal-to-noise ratio (SNR).