Mechanical loading by muscles elicits anabolic responses from bone, thus age‐related declines in muscle strength may contribute to bone fragility in older adults. We used high‐resolution peripheral quantitative computed tomography (HR‐pQCT) to determine the association between grip strength and distal radius bone density, size, morphology, and microarchitecture, as well as bone strength estimated by micro–finite element analysis (μFEA), among older men and women. Participants included 508 men and 651 women participating in the Framingham Offspring Study with grip strength measured in 2011–2014 and HR‐pQCT scanning in 2012–2015. Separately for men and women, analysis of covariance was used to compare HR‐pQCT measures among grip strength quartiles and to test for linear trends, adjusting for age, height, weight, smoking, and physical activity. Mean age was 70 years (range, 50–95 years), and men had higher mean grip strength than the women (37 kg vs. 21 kg). Bone strength estimated by μFEA‐calculated failure load was higher with greater grip strength in both men ( p < 0.01) and women ( p = 0.04). Higher grip strength was associated with larger cross‐sectional area in both men and women ( p < 0.01), with differences in area of 6% and 11% between the lowest to highest grip strength quartiles in men and women, respectively. Cortical thickness was positively associated with grip strength among men only ( p = 0.03). Grip strength was not associated with volumetric BMD (vBMD) in men. Conversely, there was a trend for lower total vBMD with higher grip strength among women ( p = 0.02), though pairwise comparisons did not reveal any statistically significant differences in total vBMD among grip strength quartiles. Bone microarchitecture (cortical porosity, trabecular thickness, trabecular number) was not associated with grip strength in either men or women. Our findings suggest that the positive association between hand grip strength and distal radius bone strength may be driven primarily by bone size. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.