Recent advances in high-resolution 3D breast imaging, namely, digital breast tomosynthesis and dedicated breast CT, have enabled detailed analysis of the shape and distribution of anatomical structures in the breast. Such analysis is critically important, since the projections of breast anatomical structures make up the parenchymal pattern in clinical images which can mask the existing abnormalities or introduce false alarms; the parenchymal pattern is also correlated with the risk of cancer. As a first step towards the shape analysis of anatomical structures in the breast, we have analyzed an anthropomorphic software breast phantom. The phantom generation is based upon the recursive splitting of the phantom volume using octrees, which produces irregularly shaped tissue compartments, qualitatively mimicking the breast anatomy. The shape analysis was performed by fitting ellipsoids to the simulated tissue compartments. The ellipsoidal semi-axes were calculated by matching the moments of inertia of each individual compartment and of an ellipsoid. The distribution of Dice coefficients, measuring volumetric overlap between the compartment and the corresponding ellipsoid, as well as the distribution of aspect ratios, measuring relative orientations of the ellipsoids, were used to characterize various classes of phantoms with qualitatively distinctive appearance. A comparison between input parameters for phantom generation and the properties of fitted ellipsoids indicated the high level of user control in the design of software breast phantoms. The proposed shape analysis could be extended to clinical breast images, and used to inform the selection of simulation parameters for improved realism.