The distribution of trapped particles in a solitary BGK wave is found by modeling the potential shape. This distribution is used in the stability analysis of a small amplitude solitary wave. It is shown that such a wave is stable for perturbation wavelengths much smaller than its width. The Lewis-Symon method is used for the normal mode perturbations localized in the BGK wave region. In this case an instability similar to the fluid beam-type instability in a homogeneous plasma takes place. © 1988 IOP Publishing Ltd.