Trabecular bone is an important load bearing material in the skeleton. It is subjected to multiaxial loading in vivo, which is a common cause of fracture in both normal and osteoporotic bone. As such, understanding the multiaxial failure behavior of trabecular bone should improve both the treatment and diagnoses of skeletal diseases related to trabecular bone. A computational modeling technique was developed to simulate mechanical tests of trabecular bone up to the yield point. These models were used to overcome the difficulties of performing mechanical tests on trabecular bone samples and obtaining sufficient numbers of experimental specimens. The level of accuracy of the computational models developed here was such that the results could be considered equivalent to experimentally measured yield properties for the specimen. The models were used to investigate the yield properties of bovine tibial trabecular bone in both biaxial normal and axial-shear loading. A Tsai-Wu criterion was able to reasonably represent the yield properties of two specimens in both the axial-shear and the biaxial loading spaces, while a Kelvin mode criterion was unable to fit the axial-shear yield data. Because the computational models allowed multiple yield points to be obtained for each specimen, these results did not depend on regressions with modulus or density as previous multiaxial failure data for trabecular bone have. The computer models were also used to investigate the locations and modes of yielding in the trabecular tissue. It was found that the mechanisms by which trabecular bone fails in on-axis (along the principal trabecular orientation) and transverse (perpendicular to the principal trabecular orientation) loading are different. Based on this finding, a multi-surface yield criterion was proposed for trabecular bone. The knowledge of trabecular bone failure gained through this investigation can be applied to improved design of total joint arthroplasty and of artificial bone material. In the long term, it should also improve the ability to diagnose and treat osteoporosis by providing a means to evaluate the strength of bone both in vitro and in vivo.