Detecting suspicious lesions in medical imaging is the important first step in computer-aided detection (CAD) systems. However, detecting abnormalities in breast tissue is difficult due to the lesion's varying size, shape, margin, and contrast with the background tissue. We focused on mass segmentation, a method that provides notable morphological features by outlining contours of masses. Accurate segmentation is crucial for correct diagnosis. Recent advancements in deep learning have improved object detection and segmentation, and these techniques are also being applied to medical imaging studies. We focused on U-net, which is a recently developed mass segmentation algorithm based on a fully convolutional network. The U-net architecture consists of (1) a contracting path to increase the resolution of the output and (2) a symmetric expanding path to better locate the region of interest. The performance of a U-net model was tested with 63 digital mammograms from INbreast, a publicly available database. We trained the model with images resized to 40x40 pixels and conducted 10-fold cross-validation to prevent overfitting. The model's performance with respect to breast density and the lesion's BI-RADS rating was also investigated. Dice coefficients (DC) were used as a performance measure to compare the predicted segmentation of the model with the ground truth. Logistic regression and an analysis of variance were performed to determine the significance of the DCs with regards to breast density and lesion behavior and to calculate the 95% confidence interval. The average DC was 0.80. The difference between DCs for BI-RADS 2 and 4c and for BI-RADS 2 and 5 were significant, suggesting that the model has more difficulty in segmenting benign lesions.