The majority of fragility fractures occur in women with osteopenia rather than osteoporosis as determined by dual‐energy X‐ray absorptiometry (DXA). However, it is difficult to identify which women with osteopenia are at greatest risk. We performed this study to determine whether osteopenic women with and without fractures had differences in trabecular morphology and biomechanical properties of bone. We hypothesized that women with fractures would have fewer trabecular plates, less trabecular connectivity, and lower stiffness. We enrolled 117 postmenopausal women with osteopenia by DXA (mean age 66 years; 58 with fragility fractures and 59 nonfractured controls). All had areal bone mineral density (aBMD) measured by DXA. Trabecular and cortical volumetric bone mineral density (vBMD), trabecular microarchitecture, and cortical porosity were measured by high‐resolution peripheral computed tomography (HR‐pQCT) of the distal radius and tibia. HR‐pQCT scans were subjected to finite element analysis to estimate whole bone stiffness and individual trabecula segmentation (ITS) to evaluate trabecular type (as plate or rod), orientation, and connectivity.Groups had similar age, race, body mass index (BMI), and mean T‐scores. Fracture subjects had lower cortical and trabecular vBMD, thinner cortices, and thinner, more widely separated trabeculae. By ITS, fracture subjects had fewer trabecular plates, less axially aligned trabeculae, and less trabecular connectivity. Whole bone stiffness was lower in women with fractures. Cortical porosity did not differ. Differences in cortical bone were found at both sites, whereas trabecular differences were more pronounced at the radius.In summary, postmenopausal women with osteopenia and fractures had lower cortical and trabecular vBMD; thinner, more widely separated and rodlike trabecular structure; less trabecular connectivity; and lower whole bone stiffness compared with controls,despite similar aBMD by DXA. Our results suggest that in addition to trabecular and cortical bone loss, changes in plate and rod structure may be important mechanisms of fracture in postmenopausal women with osteopenia.