Axial mixing in a reciprocating plate column with different amplitudes has been investigated for single-phase and two-phase (air-water) systems. Experiments were performed in water in a semi-batch scheme (no water flow) in a 1.26 m high and 101.6 mm internal diameter column. It was found that the axial dispersion coefficient is a strong function of reciprocation speed and amplitude. The presence of gas considerably affects the axial dispersion coefficient but its contribution appears to saturate at low gas flow rates and then, over a large range of gas flow rates, the axial dispersion coefficient was almost constant. Models are proposed based on experimental data to account for the effects of gas superficial velocity, amplitude and reciprocating frequency. The models predictions are compared with experimental data, obtained over a wide range of operating conditions, and the agreement between them was found to be good. A new class of nonlinear models, for which it is not necessary to have a constant dependency on each operating variable, was also used to correlate the axial dispersion coefficient. This new model allows to carry out sensitivity analysis on each operating variable.