Two different methods of measuring bone mineral content: gamma-ray scattering and gamma-ray transmission tomography have been studied using simple tissue substitute materials. Elastic photon scattering, as currently employed, relies on taking the ratio of the coherent and incoherent (Compton) scattering intensities to correct for beam attenuation. An alternative method of correction, using transmission measurements as for Compton scattering densitometry, was explored. It was demonstrated that for the 60 KeV gamma-ray from 241 Am coherent scattering, corrected in this way, was more sensitive to variations in the bone phantoms than the coherent to Compton ratio for a given dose. The improvement was probably not sufficient, however, to warrant the more complicated measurement procedure required. A first generation gamma-ray transmission tomography scanner was constructed and revealed significant differences (up to 7%) between the true linear attenution coefficients and those estimated from tomographs. This was due to photon scattering which contributed to the measured flux giving artificially high count rates. By employing a narrow, well collimated interrogating beam and maintaining a constant detector and source geometry it was still possible to characterise the phantoms using the empirically derived attenuation coefficients as, under these conditions, they were still functions of the material only. With most modern scanners using fan beam geometries of some form the influence of photon scattering will probably be even greater than on the simple system employed in this work. Experiments were also done using a 153Gd isotopic source to produce dual energy measurements using potassium hydrogen phosphate (K2HPO4) as a reference material. The results were in agreement with other work published in the literature using dual energy X-ray scans showing greater accuracy in bone mineral estimation albeit with some loss of precision.