The assessment of viscoelastic properties of soft tissues is enjoying a growing interest in the field of medical imaging as pathologies are often correlated with a local change of stiffness. To date, advanced techniques in that field have been concentrating on the estimation of the second order elastic modulus (mu). In this paper, the nonlinear behavior of quasi-incompressible soft solids is investigated using the supersonic shear imaging technique based on the remote generation of polarized plane shear waves in tissues induced by the acoustic radiation force. Applying a theoretical approach of the strain energy in soft solid [Hamilton et al., J. Acoust. Soc. Am. 116, 41-44 (2004)], it is shown that the well-known acoustoelasticity experiment allowing the recovery of higher order elastic moduli can be greatly simplified. Experimentally, it requires measurements of the local speed of polarized plane shear waves in a statically and uniaxially stressed isotropic medium. These shear wave speed estimates are obtained by imaging the shear wave propagation in soft media with an ultrafast echographic scanner. In this situation, the uniaxial static stress induces anisotropy due to the nonlinear effects and results in a change of shear wave speed. Then the third order elastic modulus (A) is measured in agar-gelatin-based phantoms and polyvinyl alcohol based phantoms.