A new ultrasonic test method is proposed to obtain elastic constants of unidirectional composite materials nondestructively. In the proposed test method, only longitudinal transducers are used to measure wave velocities by through-transmission method. An aluminum wedge and a flat aluminum rectangular block are placed on each side of the test specimen. Oblique incident longitudinal wave is transmitted from a wedge to the specimen and the mode conversions are occurred sequentially at two interfaces between the specimen and aluminium. Measuring wave velocities converted to longitudinal waves in the rectangular block give all information to determine elastic constants of the composites. In order to determine shear stiffness coefficients, transverse wave velocity is measured indirectly from received longitudinal wave. Effects of anisotropy on waves are also considered in this study.