A novel, dynamic, non-invasive, high-speed dynamic optical coherence elastography (OCE) system has been developed for quantitatively mapping tissue biomechanical properties utilizing spectral-domain optical coherence tomography (OCT) and a mechanical wave driver. This dynamic OCE technique is based on solving wave equations without speckle tracking algorithms. Using phase-resolved imaging, we demonstrate OCE can map dynamic elastic moduli of normal and neoplastic ex vivo human breast tissue. This dynamic OCE technique is used to determine in vivo skin biomechanical properties based on mechanical surface wave propagation. Quantitative Young's moduli are measured on human skin from different sites, orientations, and frequencies.