The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields. The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles. Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods, the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained. The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system. For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems, three examples involving slurry flow on three different types of river beds have been considered. The related particle simulation results obtained from these three examples have demonstrated that: 1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields; 2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed. © 2013 Central South University Press and Springer-Verlag Berlin Heidelberg.