We report on a morphological study of 192 breast masses as seen in mammograms, with the aim of discrimination between benign masses and malignant tumors. From the contour of each mass, we computed the fractal dimension (FD) and a few shape factors, including compactness, fractional concavity, and spiculation index. We calculated FD using four different methods: the ruler and box-counting methods applied to each 2-dimensional (2D) contour and its 1-dimensional signature. The ANOVA test indicated statistically significant differences in the values of the various shape features between benign masses and malignant tumors. Analysis using receiver operating characteristics indicated the area under the curve, A(z), of up to 0.92 with the individual shape features. The combination of compactness, FD with the 2D ruler method, and the spiculation index resulted in the highest A(z) value of 0.93.