Trabecular bone structural units (BSU) are known to decrease in size with age, resulting in an increase in the proportion of cement line. The mechanical consequences of these changes are unclear and could either decrease fragility by redirecting cracks or increase fragility due to preferential crack growth in the cement line. To address this question, extended finite element method modelling of an idealized 2D trabecula loaded in tension, composed of repeating hexagonal BSU, has been used to perform parametric studies of geometric properties. Assuming the cement line breaks at lower strains than the BSU, the results indicate that it is the time the crack grows within the BSU, rather than the BSU size per se, that delays the failure of a trabecula under tension. The crack path was also an important factor, with lower failure strains predicted as more of the crack propagated through the cement line. These modelling results support the notion that changes in the proportions of BSU and cement line could play a role in age-related fragility. Better experimental characterization of the trabecular BSU and cement line, both in terms of their geometry and materials properties, is needed to further investigate their contributions to fragility.