Algorithm is constructed which models single-file motion of particles interacting with each other and with the surroundings. As an example, we present the results of Brownian Dynamics simulations of the motion of cations moving through a short very narrow channel containing a device called ``gate'', which may open and close the channel.

PACS numbers: 05.10.--a, 05.10.Gg, 87.16.Uv, 05.40.Ca