Digital volumetric speckle photography (DVSP) technique is proposed to measure three dimensional displacement in solid object. Using computer tomography (CT), magnetic resonance imaging (MRI), laser- scanning confocal microscopy (LSCM) or optical coherence tomography (OCT), three dimensional volumetric images of an object with speckle characteristics before and after deformation are abtained. These three dimensional images are divided into subsets with a certain voxel array and comparable. Afterwards three- dimensional fast Fourier transform (3D- FFT) is applied to a corresponding pair of subsets. A new resultant spectrum can be constructed by a numerical interference from the two procured spectra at the spectral domain. Then another step of 3D- FFT is performed on the resultant spectrum resulting an expanded impulse function whose displacement vector experienced by the speckles contained in the original subset as a whole. This process is carried out for every corresponding pair of subsets. By detecting the position of the crests of these impulse functions, an array of displacement vectors at all every subset is obtained and the 3D displacement fields are mapped. Using simulated 3D speckle volume images, the influences of speckle size, number, subset size, image contrast and image brightness on the accuracy and precision of DVSP are analyzed by digital experiments. We apply the DVSP technique to measure the internal 3D deformation field of red sandstone sample under uniaxial compression, and the resulting displacement and deformation field contours clearly indicate the damage characters of the sample.