Elastography is a technique to assess the viscoelastic properties of tissue by measuring an acoustic wave propagating though the object. Here, the technique is applied in the course of standard MR mammography to 15 patients with different pathologies (six breast cancer cases, six fibroadenoma cases and three mastopathy cases). Low-frequency mechanical waves are coupled longitudinally into the tissue in order to obtain sufficient wave amplitude throughout the entire breast. This leads to the presence of a substantial fraction of compressional waves, which contribute to the total displacement field. It is shown theoretically that the correct evaluation of these contributions from the compressional wave is rather difficult due to the almost incompressible nature of tissue. To overcome this problem, it is proposed to apply the curl-operator to the measured displacement field in order to completely remove contributions from the compressional wave. Results from simulations and a breast phantom demonstrate the feasibility of the technique. The in vivo results show a good separation between breast cancer and benign fibroadenoma utilizing the shear modulus. Breast cancer appears on average 2.2 (P<.001) times stiffer. All breast cancer cases showed a good delineation to the surrounding breast tissue with an average elevation of a factor of 3.3 (P< 1.4 x 10(-6)). The results as obtained for the shear viscosity do not indicate to be useful for separating benign from malignant lesions.