Measuring the mechanical properties of human soft tissue is a current topic in the field of diagnostic ultrasound research. Long before ultrasound was used in medical diagnosis, palpation was the important clinical examination method, and was practiced by the ancient Egyptians about 5000 years ago. Palpation is still one of the standard examination methods performed in the modern diagnosis for the detection of inter alia breast and prostate abnormalities, because the change of the pathological state of tissue is often correlated with changes in stiffness; in particular some malignant tumors are significantly stiffer and less mobile than surrounding healthy tissue. However, the use of conventional imaging techniques such as, computer tomography, magnet resonance tomography and ultrasound, for the medical diagnosis is not directly able to measure the mechanical properties of tissue. In this work, a new imaging modality was developed which can be additionally used for the careful assessment of tumors in different soft tissues. This novel modality was named reconstructive ultrasound elastography, which is regarded as an objective imaging method not limited to small deformations and complements the manual palpation procedure for medical diagnostics. In order to obtain noninvasively quantitative mechanical properties of tissue, we proposed a new algorithm by which the spatial distribution of the relative shear modulus of tissue can be estimated from the measured deformation. From the measured displacement field the relative shear modulus distribution in the examined object can be determined in the sense of an ill-posed inverse problem. Due to the existing large deformations an algorithm was developed for the solution of the inverse problem on the basis of the nonlinear elasticity theory. The efficiency of the developed algorithm was shown using samples of poly vinyl alcohol phantoms, as well as in vivo data computed from prostate-cancer cases and compared to the histology data.