The determination of elastic constants is vital for any in‐depth study of material performances. One of the more frequently used methods for elastic constant determination involves ultrasonic velocity measurements. Although this method is convenient in isotropic materials, it involves more complicated procedures for anisotropic materials. In this study, a measurement method is introduced that does not require cutting samples for velocity measurements in different directions. This method utilizes the acoustoultrasonic technique and deduces the elastic constants of transversely isotropic materials from the time‐of‐flight of obliquely reflected echoes which are received by another transducer placed on the same surface. Analytical and numerical analyses are described which reveal the sensitivity of the results to different kinds of measurement errors. It is reported that systematic errors are most detrimental to the extraction of elastic constants, and appropriate steps are demonstrated which reduce this kind of error. This method is experimentally tested on three unidirectional graphite/epoxy composite plates. Three of the elastic constants were found using pulse‐echo velocity measurements normal to the top surface of the sample plate. The other two elastic constants were computed using acoustoultrasonic technique. The results show good agreement with nominal values of elastic constants obtained by cutting one of the tested samples.