An analysis and applications of the wave model for longitudinal dispersion are pre-sented. Asymptotic forms of the wave model are considered and analytical solutions of typical linear stationary and nonstationary problems of chemical reactor engineering interest are obtained and compared to those for the Fickian dispersion model. The wave model leads to efficient analytical solutions for linear problems, which in principle differ from the solutions of the Fickian dispersion model; only for slowly varying concentration fields do the soluctions of both models approach each other. Spatial and time moments of the concentration distribution are obtained for pulse-dispersion problems; the first three spatial moments of the mean, variance, and skewness have exact, large-time asymptotic forms in the case of Taylor dispersion. Old experiments that could not be explained with the standard dispersion model are reconsidered and explained: the change with time of the variance of a concentration pulse when the flow direction is reversed and the difference in values of the apparent axial dispersion coefficient and the backmixing coefficient in a rotating disk contactor. The experimental determination of model parameters is discussed.