We have shown, for the first time, that elastic property-porosity relationships for clean sandstones can be derived directly from microtomographic images. Moreover, we have demonstrated that it is possible to obtain a large ensemble of samples from a single tomographic image which allows measures of elastic properties to be derived over a wide range of porosities. We have shown that it is practical to generate numerical data for dry, water-saturated and oil-saturated conditions. The results for dry and water-saturated conditions are in good agreement with experimental measurements. The calculated change in the elastic properties due to fluid substitution is consistent with the exact Gassmann's equations. Overall, we have demonstrated the feasibility of combining microtomographic images with elastic calculations to accurately predict the petrophysical properties of specific rock morphologies.