We have developed a novel curve-fitting method to estimate dispersion characteristics of guided elastic waves and investigate its application to field wireline and logging while drilling (LWD) acoustic data processing. In an elastic waveguide such as a fluid-filled borehole with a logging tool, the frequency dispersion of a guided-wave mode is characterized by a monotonically varying dispersion curve bounded by its low- and high-frequency limits. The detailed behavior of the curves relates to various elastic/acoustic parameters of the complicated waveguide structure. The novelty of the proposed technique is that it simulates the multiparameter dispersion curve using a simple analytical function that has only four parameters. By adjusting the four parameters to fit the actual wave dispersion data, the wave's dispersion characteristics can be satisfactorily determined. The result of this simple approach leads to several important applications in acoustic logging. The first is to correct the dispersion effect in the shear-wave velocity from wireline dipole acoustic logging. The second application obtains P-wave velocity from the dispersive leaky compressional-wave data from wireline or LWD measurements. Third, the technique is applied to obtain shear-wave velocity from LWD quadrupole shear-wave logging. Finally, the technique is applicable to layered waveguide structures encountered in surface seismic exploration.