The anisotropy of fibrous composite materials makes it difficult to determine their elastic constants nondestructively. The unidirectional lamina, which is the basic building block of composite laminates and structures, is treated as a quasi-homogeneous orthotropic material. Determination of material properties of the unidirectional lamina is especially important because this characterization allows prediction of the properties of any multidirectional laminate. In general, the unidirectional lamina is characterized by nine independent elastic constants. Many composite materials, however, have the additional property of transverse isotropy. In such cases the number of independent constants is reduced to five. The objective of this study is to propose a method for determining these constants ultrasonically by measuring phase velocities and critical angles.