The conditions of capture and retention of charged dust particles in linear Paul traps in air at atmospheric pressure in a wide range of parameters characterizing both dynamic traps and confined particles have been found by means of Brownian dynamics. It is shown that the viscosity of a gaseous medium strongly affects capture and retention of dust particles. The simulation results are in agreement with the experimental data on the creation and retention of a stable Coulomb cluster of charged dust particles in a quadrupole trap.