A compact fiber-optic Sagnac interferometer detects a genuine mechanical wave instead of displacement.This avoids the further signal processing for wave signal extraction as in displacement-based detection systems. However, due to both interfering lights coming from sample surface, the collected light in a fiber-optic-based Sagnac interferometer system is very weak when applied to biological tissue, where the refractive index of tissue and air are close. The objective of this paper is to study the feasibility using a compact fiber-optic Sagnac interferometer to detect vibrational waves on a biological tissue surface. An actuator made with a 10mm x 10mm x 3mm piezoelectric chip loaded on a 3D-printed polymer-made prism-shaped wedge (lcm xlcm xlcm) was used for ultrasound surface wave excitation. A bulk copolymer-in-oil phantom (100mm diameter with 27mm height) was used to mimic biological tissues. A compact fiber-optic-based interferometer was used to detect the propagation of surface waves in the tissue mimicking phantom and the wave propagation speeds were determined based on the wave detection. Young's modulus was calculated based on the measured wave speed on the phantom surface. A tensile testing machine was used to measure the Young's modulus in a compression mode as a comparison. The results were compared.