The modulus of elasticity of cubes of cancellous bone, tested in three orthogonal directions, was measured along with apparent density, fabric (measured using image analysis techniques), connectivity and mineral volume fraction. Multiple regression was used to relate Young's modulus and the explanatory variables. The most important explanatory variable was apparent density; fabric was also important. Connectivity was highly correlated with apparent density, and so it is difficult to assign relative weights to these two variables. However, both have a significant, and separate, effect on Young's modulus. The total variance in Young's modulus explained by these three variables was about 85 per cent. This implies that other explanatory variables are either unimportant or highly correlated with the variables listed above. Mineral volume fraction is shown to be an unimportant variable, and arguments are produced why this is to be expected, even though it is highly important in explaining the variation in Young's modulus of compact bone.