A technique is described for the determination of the elastic constants of a composite specimen by measuring, in an immersion tank, the velocities of ultrasonic waves propagating in various directions in the specimen. The theoretical basis of the method, the restrictions on specimen geometry, and possible sources of inaccuracy in the measurement and interpretation of data, are all discussed. Typical results are illustrated by data for a high modulus carbon fiber reinforced epoxy. A discussion is given of the use of ultrasonic techniques for material characterization. In particular, methods are discussed for identifying and quantifying specimen homogeneity, symmetry, degree of misorientation, and defect content. Extension of the techniques to the determination of viscoelastic properties, and the associated theoretical and practical problems, is also considered.