Tissue elastography characterizes tissue mechanical properties, which can provide important information for diagnosis. While popular methods track shear wave propagation inside tissue, this paper proposes a method to estimate elasticity by measuring group velocity of the surface Raleigh wave. This method features noncontact, noninvasive and low-cost and have a great potential for clinic applications. By measuring the impulse response of a tissue simulating phantom at multiple points along the direction of surface wave propagation, the group velocity is estimated to be 12.61 m/s, therefore Young's modulus is 526 kPa. This result is consistent with the results obtained by Continuous Wave (CW) excitation.