Cortical bone is a compact tissue with anisotropic macroscopic mechanical properties determined by a microstructure and the quality of a mineralised collagen matrix. Anisotropic elastic properties and strength are usually measured on different groups of sample which can hardly be pooled; as a consequence little is known on the relationships between strength and elasticity in the different anatomical directions. A method is presented to measure on a same cortical bone sample: (1) Young's modulus and strength (sigma(max)) in the longitudinal direction; (2) stiffness (C(11)) in the transverse direction. Longitudinal and transverse direction are taken along and perpendicular to the diaphysis axis, respectively. Ultrasonic techniques yield Young's modulus (E(a)) and C(11); three-point bending tests yield Young's modulus (E) and sigma(max). The relationships between strength, elasticity and density and their anatomical distributions were investigated for 36 human femur samples. (i) A marginal negative correlation was obtained for E(a) and C(11) (R=-0.21; p=0.08); (ii) sigma(max) was significantly correlated to E and E(a) (R approximately 0.5; p<0.005) but not to C(11) (p>0.2); (iii) density was not correlated with E and moderately with strength (R=0.38; p<0.3). Small density variability (+/-30 kg m(-3)) may partly explain the results. The techniques presented are suited to a systematic characterization of bone samples.