Tissue stiffness is a key biomechanical property that can be exploited for diagnostic and therapeutic purposes. Tissue stiffness is typically measured quantitatively via shear wave elastography or qualitatively through compressive strain elastography. This work focuses on merging the two by implementing an uncalibrated stress sensor to allow for the calculation of Young’s modulus during compression elastography. Our results show that quantitative compression elastography is able to measure Young’s modulus values in gelatin and tissue samples that agree well with uniaxial compression testing.