The multi-particle simulation program ITSIM version 4.0 takes advantage of the enhanced performance of the Windows 95 and NT operating systems in areas such as memory management, user friendliness, Ñexibility of graphics and speed, to investigate the motion of ions in the quadrupole ion trap. New features and capabilities signiÐcantly broaden its applicability. The simulation program can provide help in understanding fundamental aspects of ion trap mass spectrometry and both precede experiments and assist in directing their course. It also has didactic value in elucidating and allowing visualization of ion behavior under a variety of experimental conditions. ITSIM 4.0 provides easy access to ion simulations for all users through a dramatically improved user interface. The program uses the improved Euler method to calculate ion trajectories as a numerical solution to the Mathieu di †erential equation. The Windows version can simultaneously simulate the trajectories of ions with a virtually unlimited number of di †erent mass-to-charge ratios, up to a maximum of 600 000 ions, and hence allow realistic mass spectra, ion kinetic energy distributions, phase-of-ejection distributions and other experimentally measurable properties to be simulated. The simulated data are used to obtain mass spectra from mass-selective instability scans and by Fourier transformation of image currents induced by coherently moving ion clouds. Field inhomogeneities arising from exit holes, electrode misalignment, imperfect electrode surfaces or alternative trap geometries can be simulated with the program. Non-zero angle scattering in the hard-sphere collision model allows simulations involving collisional cooling to be performed. Complete instruments, from an ion source through the ion trap mass analyzer to a detector, can be simulated. Some typical applications of the simulation program are presented and discussed. Such features as the mass-selective instability scan mode, mass-range extension via resonant ion ejection, r.f. and d.c. ion isolation and non-destructive detection are shown. Comparisons are made between the simulated and experimental results, for example in mass-selective photodissociation. Fourier transform experiments and a novel six-electrode ion trap mass spectrometer illustrate cases in which simulations precede reduction to practice.