An apparatus for providing assessment indices related to bone strength which are useful in predicting the risk of bone fracture. The apparatus measures the mineral density of bone (BMD) by means of X-rays, while the propagation speed of sound V in the bone and bone thickness d are measured by means of ultrasonic waves. The bone mineral content per unit volume, i.e. the bone volume density .rho., is computed from the bone mineral density (BMD) and the thickness of the bone. An assessment value E is then computed based on V and .rho..