In dynamic optical coherence elastography (OCE), surface acoustic waves are the predominant perturbations. They constrain the quantification of elastic modulus to the direction of wave propagation only along the surface of tissues, and disregard elasticity gradients along depth. Longitudinal shear waves (LSW), on the other hand, can be generated at the surface of the tissue and propagate through depth with desirable properties for OCE: (1) LSW travel at the shear wave speed and can discriminate elasticity gradients along depth, and (2) the displacement of LSW is longitudinally polarized along the direction of propagation; therefore, it can be measured by a phase-sensitive optical coherence tomography system. In this study, we explore the capabilities of LSW generated by a circular glass plate in contact with a sample using numerical simulations and tissue-mimicking phantom experiments. Results demonstrate the potential of LSW in detecting an elasticity gradient along axial and lateral directions simultaneously. Finally, LSW are used for the elastography of ex vivo mouse brain and demonstrate important implications in in vivo and in situ measurements of local elasticity changes in brain and how they might correlate with the onset and progression of degenerative brain diseases.