Collisional cooling radio frequency (RF) multipoles are widely used in mass spectrometry, as ion guides and two-dimensional ion traps. Understanding the behavior of ions in these devices is important in choosing a multipole configuration and optimizing its performance. We have developed a computer model based on ion trajectory calculations in the RF multipole electric field, taking into account ion-ion and ion-neutral interactions. The two-dimensional model for idealized infinite RF multipoles gives an accurate description of the ion density distribution. We consider first a basic case of a single m/z ion cloud in the two-dimensional RF quadrupole after equilibrium is reached. Approximate theoretical relationships for the ion cloud configuration in the two-dimensional ion trap are tested based on the simulation results. Next we consider the case of an ion cloud consisting of several different m/z ion species. The ion relaxation dynamics and the process of establishing the stratified ion density distribution are observed. Simulations reveal that the ion kinetic energy relaxation dynamics are dependent on the ion population and bath gas pressure. The equilibrium distribution agrees well with the ion stratification theory, as demonstrated by simulations for RF quadrupole and octopole two-dimensional ion traps.