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Two limitations hamper performance of deep architectures for classification and/or detection in medical imaging: (i) the small amount of available data, and (ii) the class imbalance scenario. While millions of labeled images are available today to build classification tools for natural scenes, the amount of available annotated data for automatic breast cancer screening is limited to a few thousand images, at best. We address these limitations with a method for data augmentation, based on the introduction of random elastic deformations on images of mammograms. We validate this method on three publicly available datasets. Our proposed Convolutional Neural Network (CNN) architecture is trained for mass classification - in a conventional way -, and then used in the more interesting problem of mass detection in full mammograms by transforming the CNN into a Fully Convolutional Network (FCN).