Abstract: This paper derives the characteristic equations, dispersion curves and mode shapes of Lamb waves in plates and longitudinal mode guided waves in pipes in details by solving the Navier equation for different waveguide structures and boundary conditions. By comparing the characteristic equations of Lamb waves and longitudinal mode guided waves, it can be found that for pipes and plates that have the same material and wall thickness, the characteristic equations of longitudinal modes in pipes can be simplified to the characteristic equations of Lamb waves in plates when the pipe radius is large enough. Moreover, through the comparison of dispersion curves, it has been found that the dispersion relations of pipes gradually approach to the dispersion relations of plates. Particularly, the longitudinal mode L (0, 1) in pipes approaches to the A₀ mode in plates, and the longitudinal mode L (0, 2) in pipes approaches to the S₀ mode in plates.