Due to the ability of modelling large deformations and the ease of dealing with moving boundary conditions, the material point method is gaining popularity in geotechnical engineering applications. In this paper, this promising Lagrangian method is applied to hydrodynamic problems to further explore its potential. The collapse of water columns with different initial aspect ratios is simulated by the material point method. In order to test the accuracy and stability of the material point method, simulations are first validated using experimental data and results of mature numerical models. Then, the model is used to ascertain the critical aspect ratio for the widely-used shallow water equations to give satisfactory approximation. From the comparisons between the simulations based on the material point method and the shallow water equations, the critical aspect ratio for the suitable use of the shallow water equations is found to be 1.