The microtextural symmetry of dry human cortical bone was found to be consistent with hexagonal symmetry, based on microstructural observations as well as on the ultrasonic velocity measurements at 5 MHz and at room temperature using a pulse transmission method. Five independent elastic stiffness constants were obtained therefrom and are (in 10¹⁰ N/m²): c₁₁ = 2.34, c₃₃ = 3.25, c₄₄ = 0.871, c₁₂ = 0.906, c₁₃ = 0.911. Microhardness measurements on the cross section of the bone show that it is ‘intrinsically’ uniform from the endosteal to the periosteal side and for the four quadrants. The dependence of the elastic stiffnesses on the polar angle is plotted to show how the elastic stiffnesses are interrelated to the orientations in the bone. Characteristics of ultrasonic wave propagation in the bone were shown to be somewhat analogous to those in a fiber-reinforced composite material; the bone filters and polarizes ultrasonic waves.