Elastic imaging intends to measure Young’s modulus (tissue stiffness) or bulk modulus (tissue compressibility) of tissue subjected to an applied strain of several percent. Underlying elastic imaging is the assumption of a linear stress/strain relationship without hysteresis or other time-dependent behavior. Perfused tissue is a composite material comprised of a solid matrix of cells, fibers, interstitial fluid (occupying up to 50% of the tissue volume and varying slowly with time), arterioles (pulsating high-pressure spaces that occupy 0.1% of the tissue volume), capillaries, and venules (low-pressure spaces that occupy up to 3% of the tissue volume varying with respiration). This talk will speculate on the nonlinear, nonstationary stress/strain relationships expected from dependent tissues (legs), pressurized tissues (breast tumors), and other living, perfused tissues. The pressure versus strain curve from each tissue voxel allows the measurement of arteriolar and venular volumes and pressures, and interstitial pressure within the tissues. These volumes and pressures may be key to classifying pathologies.