The long term objective of this research is to develop a method to infer and image tissue hardness using ultrasound. This method would bring new quantitative information about the condition of a tissue, similar to what palpation does qualitatively when sensing "hard" tumor of a muscle under contraction. It consists essentially in measuring the deformation induced through an external force, the deformation being large in a compliant (i.e. soft) material and smaller in a rigid (hard) one. As proposed here, tissue deformation is assessed by tracking the spatio- temporal changed induced by the compression force on the ultrasound speckle patterns. Technically, this application is for developing a model-based approach to compute the elasticity distribution (also called the elastogram) using ultrasound speckle replacement data. First, it is proposed to study a direct elasticity problem; here the aim is to provide an analytical framework and a computer model of image formation for speckle correlation and motion, assuming an elastic scattering medium subjected to deformations. From a theoretical point of view, this will serve to better understand the complex relationship between the spatio-temporal changes in ultrasound signals and underlying tissue motion. From a practical standpoint, this will serve to develop and test tissue motion estimators based either on speckle correlation measurement or on optical flow. Tissue motion estimation is the first step in solving the inverse elasticity problem which can be stated as: determining the spatial distribution of elasticity that could best reproduce the estimated tissue motion under constraints provided by the elasticity equations and boundary conditions. It is proposed to develop an iterative procedure to seek the optimal elastogram, i.e. a non linear minimization method based on the image formation model, the optical flow equation and the elasticity equations. It is also proposed to study the feasibility of in vivo elastography of the prostate. This research on a method to infer tissue hardness will be conducted using computer modeling, and the method will be validated on a phantom model. The feasibility of in vivo prostate elastography will be examined through a subcontract project conducted in Lyons, France (Dr. jean Yves Chapelon) using ultrasound signals currently being acquired in a separate study investigating hyperthermia induced by high intensity focused ultrasound.