Although bone strength and modulus are known to be influenced by both volume fraction and mineral content (ash fraction), the relative influence of these two parameters remains unknown. Single-parameter power law functions are used widely to relate bone volume or ash fraction to bone strength and elastic modulus. In this study we evaluate the potential for predicting bone mechanical properties with two-parameter power law functions of bone volume fraction (BV/TV) and ash fraction (α) of the form y = a(BV/TV)^b α^c (where y is either ultimate strength or elastic modulus). We derived an expression for bone volume fraction as a function of apparent density and ash fraction to perform a new analysis of data presented by Keller in 1994. Exponents b and c for the prediction of bone strength were found to be 1.92 ± 0.02 and 2.79 ± 0.09 (mean ± SE), respectively, with r² = 0.97. The value of b was found to be consistent with that found previously, whereas the value of c was lower than values previously reported. For the prediction of elastic modulus we found b and c to be 2.58 ± 0.02 and 2.74 ± 0.13, respectively, with r² = 0.97. The exponent related to ash fraction was typically larger than that associated with bone volume fraction, suggesting that a change in mineral content will, in general, generate a larger change in bone strength and stiffness than a similar change in bone volume fraction. These findings are important for interpreting the results of antiresorptive drug treatments that can cause changes in both ash and bone volume fraction.