In the present study, two goniometry based immersion techniques have been compared for the measurement of elastic constants in isotropic and transversely isotropic materials. Measurements were carried out on transversely isotropic unidirectional (glass-epoxy and graphite-epoxy) composite materials. From the measured velocity data, the elastic constants were determined through a numerical inversion. These techniques (through-transmission and back-reflection) were verified using contact testing, mechanical testing, rule of mixtures estimation and the data provided by the manufacturers. The results obtained and the limitations of each of these techniques are discussed. © 2004 Elsevier Ltd. All rights reserved.