Resonant ultrasound spectroscopy is the study of spectra obtained by forced mechanical resonance of samples by swept frequency excitation. A novel apparatus is used to measure the amplitude/frequency resonance spectrum of a right rectangular parallelepiped specimen of AS4/3501-6 carbon epoxy composite material ([0, 60, 120]192 lay-up) at 1 degrees C intervals between - 177 degrees C and 25 degrees C. It is important to know the mechanical properties of this material at low temperatures for underwater, polar and space applications. The spectra indicate increasing stiffness with decreasing temperature and phase transitions. The damping decreases slightly with decreasing temperature. Analysis of the resonance spectrum, calculation of theoretical resonance spectrum, and computation of elastic stiffness tensor will be discussed.