A majority of the current experimental techniques for measuring damping employ either flexural or torsional vibrations. Both produce a non-homogeneous strain field. If the material damping is strain independent (linear), then the measured quantity is a true representation of the intrinsic material damping. However, if the material damping is strain dependent (non-linear), then the measured quantity will be a measure of the volume-averaged (global) intrinsic material damping. This paper presents a new technique for measuring the intrinsic material damping by employing a homogeneous strain field by subjecting specimens to a time-harmonic uniform uniaxial tension using an MTS apparatus. Using the elementary theory of Fourier transforms, the phase difference between the stress and the strain was resolved in the frequency domain (rather than in the time domain) to an accuracy of 9.587 × 10-5 rad (5.49 × 10-3 deg); the frequency range of this study was 0.5 to 10 Hz. A flexural apparatus was also developed to measure damping in a well-known logarithmic decrement technique. Both apparatuses incorporated digital data acquisition and were fully automated. The application of both techniques was illustrated by measuring the damping of a [ ± θ]s metal-matrix composite as a function of ply-angle, 9. Unidirectional Pitch 55 graphite fibers in a matrix of 6061 aluminum were tested for the following values of θ: 0°, 15°, 30°, 45°, 60°, 75°, and 90°. In addition, the damping of two  graphite/magnesium composites was measured in flexure. Following a recent calculation by Ni and Adams, expressions for axial damping were derived based on the damping properties of a lamina. In addition, the expressions derived by Ni and Adams were extended to include stress and strain terms that had been previously neglected. For both the flexural and axial damping of the metal-matrix composites tested, satisfactory agreement between the theory and experiment was observed.