The theory for flow and sediment transport in a curved channel that was presented by Sun et al. , paper I of this two-part study, was used to develop a computer model for meandering rivers with multiple sediment grain sizes. The model, which is based on the linear theory of Johannesson and Parker <1989> for meandering rivers, takes into account the effects of alternate bars. Therefore this is one of the first models that can be used to simulate bar-bend interactions and their relationships with both the initial growth and the long-term development of meandering rivers. Unlike the previous theoretical studies of Blondeaux and Seminara <1985> and Johannesson and Parker <1989>, the results show that the initial growth of meandering rivers is controlled primarily by the curvature-related instabilities, and the influence of alternate bars on the initial development of meander loops appears to be negligible. The simulations also show that under certain conditions, meandering rivers do evolve toward a resonant state. It appears that finite amplitude perturbations are needed to enhance the initial development of alternate bars in the channel in order for the river to develop toward a bar-bend resonance state. The model includes the transport and sorting of sediment with a distribution of grain sizes. Heterogeneities in the sedimentary material deposited in the floodplain, as a result of meandering river migration, are realistically simulated. ¿ 2001 American Geophysical Union