Trapping ions injected into a quadrupole ion trap (QIT) by increasing the trapping r.f. voltage on a ring electrode is an effective and widely recognized method of interfacing an ion trap with pulsed ion sources such as matrix-assisted laser desorption/ionization (MALDI). In this paper, the problem of mass discrimination during the injection and trapping of ions by the increasing r.f. field was studied both experimentally and by numerical simulation using SIMION software. For a MALDI/QIT interface design with a remote external ion source described here, experiments with polyethylene glycol (PEG 1000 and PEG 1500) showed little mass discrimination for trapping ions in a wide mass range (500-2000 Dn) for a broad range of experimental conditions, which include kinetic energies of 5-40 eV for the injected ions and an r.f. voltage of 400-4000 Vo-p amplitude ramped at a rate of 30-140 Vo-p mus-1. In the numerical simulation, complex and sharp dependences of the trapping efficiency on the phase of the r.f. voltage and initial kinetic energy of ions were observed. However, after averaging over the r.f. phase and over a reasonable range of kinetic energy, the simulation resulted in relatively constant and high values for the trapping efficiency (normally 0.2-0.3) for any mass and kinetic energy considered, which are consistent with the weak sensitivity to injection parameters observed in the experiment. A simple model for the qualitative description of ion injection and trapping is suggested that relies on phase interaction of injected ions with the r.f. field rather than on collisions with the buffer gas molecules to decrease the ion kinetic energy.