An elastic perfectly plastic mathematical model for the behavior of bone tissue is presented in an attempt to reconcile previous discrepancies in the literature in the calculated ultimate tensile strength from bending and tensile tests. Specimens of round and square crosssections were tested in bending to demonstrate the effect of cross-sectional shape on initiation of plastic flow and consequent increase in moment carrying capacity. Tensile tests on specimens with circular cross-section were made to show that the bone tissue can indeed demonstrate considerable plastic deformation.