In this paper we examined efficiency of one of the method for numerical inversion of the Laplace transform: the Gaver-Stehfest method to find solution an one-dimensional gas flow model with axial dispersion. Algorithm was used to determine values of the axial dispersion coefficients DL and Pèclet numbers Pe on the basis of the pulse tracer technique. Obtained results of Pèclet numbers indicate that the gas flow is neither plug flow nor perfect mixing under operation condition. Numerical results are provided to confirm the efficiency of the presented method. Calculations were performed with the use of the CAS program type (Maple^®).