A bone assessment apparatus provides a precise bone assessment based on the attenuation factor of an ultrasonic wave which has passed through a bone of a patient. A transmitting transducer and a receiving transducer are positioned at either side of the bone respectively, and an ultrasonic wave is irradiated to the bone, and passes therethrough. A transmitter/receiver provides an attenuation spectrum of the ultrasonic wave and determines a reference frequency f.sub.p peculiar to the patient at which the attenuation factor is minimum. A gradient .DELTA. of the attenuation spectrum is calculated based on the difference between the attenuation factor .alpha..sub.p at the reference frequency f.sub.p and the attenuation factor .alpha..sub.q at a frequency f.sub.q which is spaced apart by a predetermined value from the reference frequency f.sub.p. A density index .rho..sub.I is also calculated which is a gradient of the attenuation spectrum per unit thickness of the bone.