Surgical reconstruction of natural-appearing breasts is a challenging task. Currently, surgical planning is limited to the surgeon's subjective assessment of breast morphology. Therefore, it is useful to develop objective measurements of breast contour. In this paper, a novel quantitative measure of the breast contour based on catenary theory is introduced. A catenary curve is fitted on the breast contour (lateral and inferior) and the key parameter determining the shape of the curve is extracted. The new catenary analysis was applied to pre- and post-operative clinical photographs of women who underwent tissue expander/implant (TE/Implant) reconstruction. A logistic regression model was developed to predict the probability that the observed contour is that of a TE/Implant reconstruction from the catenary parameter, patient age, and patient body mass index. It was demonstrated that the parameters contain useful information for distinguishing TE/Implant reconstructed breasts from pre-operative breasts.