As a non-destructive test, the ultrasonic pulse velocity measure is one of the convenient tools suggested to estimate elasticity and strength properties of rocks. Since the experimental procedure and identification process cover various uncertainty sources, an extensive measurement uncertainty analysis is required to determine the variations in the testing procedure and measurement. As a generally accepted document for the measurement uncertainty, the Guide to expression of uncertainty in measurement (GUM)' recommends Taylor and Monte Carlo methods to evaluate the measurement uncertainties. In this study, both random and systematic uncertainties encountered in ultrasonic wave propagation are analysed and appraised. Starting from the conventional methods recommended in GUM and further approaches proposed previously, a copula-based evaluation procedure is proposed in order to improve the consideration of dependencies in the measurement data.