Lanthanum-gallium tantalate (LGT) is a member of the LGX crystal family (langasite, langanite, and langatate) known for high-quality factor and stability at higher temperatures. These characteristics enable filters and sensors for use in harsh environments. Accurate values for the second-order material constants are required for electromechanical modeling of such devices. A sufficient set of bulk acoustic wave (BAW) propagation velocities have been measured in cube-shaped samples to obtain the full set of second-order elastic and piezoelectric material constants along with the experimental uncertainties. The cross correlation method was used to accurately measure the time-of-flight (TOF) values between the first two back-wall echoes under a constant room-temperature environment. The calculated BAW velocities and extracted material constants show good agreement with earlier work.