Common breast lesions have different elasticity properties. Segmentation of contours of breast lesions from elastography and B mode images by incorporating variational level set method is involved in the proposed work. After segmentation, strain and shape features, such as differences in area, perimeter, and contour and width to height difference and solidity, as well as texture features like contrast, entropy, standard deviation, dissimilarity, homogeneity and energy, are estimated. A nonlinear fuzzy inference system is applied for classifying the breast lesions as benign cyst, benign solid mass, or malignant solid mass. Detection of malignant solid masses is our primary objective. A classification accuracy of 83% is obtained. One hundred percent sensitivity is reported. It can be concluded that the proposed fuzzy-based classification technique can be used as an aid for the automated detection of breast lesions.