The main objective of this article is to introduce a new nonlinear elastography based classification method for human breast masses. Multi-compression elastography imaging is elucidated in this study to differentiate malignant from benign lesions, based on their nonlinear mechanical behavior under compression. Three classification parameters were used and compared in this work: a new nonlinear parameter based on a power-law behavior of the strain difference between breast masses and healthy tissues, mass-soft tissue strain ratio and the mass relative volume between B-mode and elastography imaging. Using 3D elastography, these parameters were tested in vivo. A pilot study on 10 patients was performed, and results were compared with biopsy diagnosis as a gold standard. Initial elastography results showed a good agreement with biopsy outcomes. The new estimated nonlinear parameter had an average value of 0.163±0.063 and 1.642±0.261 for benign and malignant masses, respectively. Strain ratio values for the benign and malignant masses had an average value of 2.135±0.707 and 4.21±2.108, respectively. Relative mass volume was 0.848±0.237 and 2.18±0.522 for benign and malignant masses. In addition to the traditional normal axial strain, new strain types were used for elastography and constructed in 3D, including the first principal, maximum shear and Von Mises strains. The new strains provided an enhanced distinction of the stiff lesion from the soft tissue. In summary, the proposed elastographic techniques can be used as a noninvasive quantitative characterization tool for breast cancer, with the capability of visualizing and separating the masses in a three dimensional space. This may reduce the number of unnecessary painful breast biopsies.