Changes in tissue elasticity are generally correlated with pathological phenomena. Similarly, diffuse liver disease significantly reduces the elasticity of the liver progressively, yet, they appear normal in conventional ultrasound examinations. Quasi-static elastography is popular in clinical applications to visualize regions with different relative stiffness. However, the limitation of this technique is that it provides only qualitative information. To overcome this, we used a reference layer with known stiffness, sandwiched between the transducer and the tissue surface, and used it to normalize and quantitatively image the unknown modulus of the examined tissue. The performance of the method was studied through simulations and experiments on agar-gelatin phantoms having the Young's modulus range appropriate for liver application, using a commercially available reference layer and considering its modulus contrast efficiency. The results suggest that using this approach it is feasible to perform quantitative imaging of the underlying target with an error less than 12%. © 2018 IEEE.