We report a method for measuring shear wave velocity in soft materials using phase stabilized swept source optical coherence tomography (PhS-SSOCT). Wave velocity was measured in phantoms with various concentrations of gelatin and therefore different stiffness. Mechanical waves of small amplitudes (∼10 μm) were induced by applying local mechanical excitation at the surface of the phantom. Using the phase-resolved method for displacement measurement described here, the wave velocity was measured at various spatially distributed points on the surface of the tissue-mimicking gelatin-based phantom. The measurements confirmed an anticipated increase in the shear wave velocity with an increase in the gelatin ...