A simple model is presented for the gravity-driven motion of a particle in a two-dimensional vertical channel with rough walls, where the dynamics is described by a 2D nonlinear mapping. It is shown that if the collisions with the channel walls are inelastic then the particle reaches a steady state where it falls with a constant average velocity. If the collisions are elastic, then the dynamics is governed by a 2D area-preserving mapping that exhibits a complex behavior in phase space. The model is then extended to include the case of several vertical plates falling under gravity inside a channel, where a steady state is reached with a parabolic velocity profile across the channel.