There is increasing evidence showing the involvement of mechanical-transduction processes in the interplay between shape-related strains and expression of the genome in living tissues. However, tools allowing long term control of physiological mechanical stress from the inside the tissues lack the investigation of the impact of such processes in organisms. This work presents the feasibility of obtaining a complete 2D-map of the stress applied to an elastic soft tissue according to the Hooke's law (σ = E.ε, where σ is the stress, E is the Young's modulus and ε is the strain). By combining the concepts of dynamic elastography (Supersonic Shear Imaging - SSI) and static elastography, both the elastic modulus (E) and strain (ε) can be retrieved respectively. The SSI technique is based on the combination of radiation force induced by an ultrasonic beam and an ultrafast imaging sequence (5000 frames/s) capable of catching in real time the propagation of the resulting shear waves. Then by measuring the shear wave velocity (Vs), the complete 2D elasticity map can be retrieved through the well known expression E = 3ρVs², where ρ represents the density of the medium. For the static elastography part, the tissue is slightly compressed and a ultrasound image is acquired before and after static compression. The cross-correlation between these two ultrasound images allows the determination of the accurate 2D strain map. Experiments are performed on diverse types of agar-gelatin phantoms mimicking soft tissues which present inclusions with different levels of stiffness. Results are also presented on ex vivo tissues (muscles, liver) and the influence of the boundary conditions on measurements is discussed. The mapping of quasi-static stress applied to biological tissues could play a key role in the understanding of tumour mechanical-transduction processes where mechanical stress may induce changes within the tumour structure.