Masses are one of the prevalent early signs of breast cancer, visible in mammogram. However, its variation in shape, size, and appearance often creates hazards in proper diagnosis of mammographic masses. This study analyses the 2D singularities of masses and their surrounding regions with Ripplet‐II transform to classify them as benign and malignant. Since benign and malignant masses may change the orientation patterns of normal breast tissues differently, several textural features including Ripplet‐II coefficients and statistical co‐variates, derived from the Ripplet‐II transformed images, are extracted to quantify the texture information of mammographic regions. The important features are then selected using stepwise logistic regression technique and evaluated using linear discriminant analysis and support vector machine with a ten‐fold cross‐validation. The best performance in terms of the area under the receiver operating characteristic curve of 0.91 ± 0.01 and 0.83 ± 0.01 and accuracy of 87.28 ± 0.02 and 75.60 ± 0.01 are obtained with the proposed method while experimenting with 58 images from the mini‐MIAS and 200 images from the Digital Database for Screening Mammography database, respectively.