The conflicting conclusions regarding the relationship between the tensile and compressive strengths of trabecular bone remain unexplained. To help resolve this issue, we compared measurements of the tensile (n = 22) and compressive (n = 22) yield strengths, and yield strains, of trabecular bone specimens taken from 38 bovine proximal tibiae. We also studied how these failure properties depended on modulus and apparent density. To enhance accuracy, trabecular orientation was controlled, and each specimen had a reduced section where strains were measured with a miniature extensometer. We found that the mean yield strength was 30% lower for tensile loading. However, the difference between individual values of the tensile and compressive strengths increased linearly with increasing modulus and density, being negligible for low moduli, but substantial for high moduli. By contrast, both the tensile and compressive yield strains were independent of modulus and density, with the yield strain being 30% lower for tensile loading. Thus, the difference between the tensile and compressive strengths of bovine tibial trabecular bone depends on the modulus, but the difference between yield strains does not. This phenomenon may explain in part that conflicting conclusions reached previously on the tensile and compressive strengths of trabecular bone since the mean modulus has varied among different studies. Realizing that our data pertain only directly to bovine tibial trabecular bone for longitudinal loading, our results nevertheless suggest that failure parameters based on strains may provide more powerful and general comparisons of the failure properties for trabecular bone than measures based on stress.