Normal and pathological breast tissue samples were scanned using a Photon Transmission Tomography (PTT) technique in order to determine their averaged photon linear attenuation coefficients (mu). Subsequent to being freeze-dried the samples were examined, using a high purity germanium detector (HPGe) and the gamma-rays of energy 59.5 keV from an americium source, and the results were corrected for the water reduction by the use of the Mixture Rule. The ratio of our experimental findings to the published data for mu for various breast tissues were 88, 96 and 88% for adipose, glandular and tumour tissues, respectively. The mean accuracy in our study, investigated relative to standard chemical compounds, was about 3%. The water content of each tissue type was determined as the weight loss during the freeze drying process. This work was initiated in order to evaluate the suitability of new tissue substitute materials for mammography applications.