The study of variation in biomechanical properties is a significant diagnostic tool for examining malignancy in tissues. Elastography is a potential technique that is used for qualitative and quantitative assessment of abnormal tissues. Optical coherence elastography is a highly efficient and promising technique for inspecting soft biological tissues with microscale resolution. In the present work, we report the elastographic measurement of tissue-mimicking phantoms of varying stiffness using reflection mode holographic imaging. The sinusoidal surface excitation is produced by an electromechanical actuator on the sample over a set of frequencies and the phase map of the surface wave is reconstructed using a phase-shifting algorithm. The preliminary results are well correlated with previously reported literature. The current work has high potential applications for quantifying the biomechanical properties of in-vivo and ex-vivo tissues in clinical practice. © 2023 SPIE.