In order to understand complex-hierarchical biomaterials such as bones and teeth, it is necessary to relate their structure and mechanical-properties. We have adapted electronic speckle pattern-correlation interferometry (ESPI) to make measurements of deformation of small water-immersed specimens of teeth and bones. By combining full-field ESPI with precision mechanical loading we mapped sub-micron displacements and determined material-properties of the samples. By gradually and elastically compressing the samples, we compensate for poor S/N-ratios and displacement differences of about 100nm were reliably determined along samples just 2~3mm long. We produced stress-strain curves well within the elastic performance range of these materials under biologically relevant conditions. For human tooth-dentin, Young's modulus in inter-dental areas of the root is 40% higher than on the outer sides. For cubic equine bone samples the compression modulus of axial orientations is about double the modulus of radial and tangential orientations (20 GPa versus 10 GPa respectively). Furthermore, we measured and reproduced a surprisingly low Poisson's ratio, which averaged about 0.1. Thus the non-contact and non-destructive measurements by ESPI produce high sensitivity analyses of mechanical properties of mineralized tissues. This paves the way for mapping deformation-differences of various regions of bones, teeth and other biomaterials.