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Inexpensive, commercially produced devices that directly measure bone strength in vivo are not currently available. Mechanical response tissue analysis (MRTA), a unique prototype device, is an in vivo vibrational test that measures transverse bending stiffness (a measure of whole bone strength expressed as the product of estimated Young's modulus of elasticity and cross-sectional moment of inertia, EI, Nm2) at ulna midshaft. We compared speed of sound (SOS; [m/s]) in ulna cortical bone using a commercially available axial transmission quantitative ultrasound (QUS) device with EI using MRTA. Dual-energy X-ray absorptiometry (DXA) was used to provide an estimate of ulna size (cm2), bone mineral content (BMC; [g/cm]) and areal bone mineral density (BMD; [g/cm2]). The objective of the study was to determine if ulna SOS—alone or in combination with BMD from DXA—was correlated with ulna EI, thus becoming a surrogate measure of transverse bending stiffness, and thus whole bone strength. Data were collected from 138 female volunteers (18–86 yr). EI and SOS were significantly correlated, r = +0.218, p = 0.01, but r2 was very low, 4.8%. SOS and total ulna BMD were combined to estimate elastic modulus, which correlated with EI, r = +0.377, p < 0.0001; however, the correlation was not significantly better than with SOS alone. We conclude that axial transmission QUS is not a strong surrogate in vivo technique for estimating transverse bending stiffness.