A new simulation program 'MATCH' has been developed for a detailed analysis of low-energy ion scattering (LEIS) and recoiling data. Instead of performing the full calculation of the three-dimensional trajectories through the sample from the ion source towards the detector, incoming trajectories as well as reversed-time outgoing trajectories are calculated, separately. Finally, these trajectories are matched to obtain the yield. The program has been tested for spectra and azimuthal scans of scattering and recoiling events of various sample species in different scattering geometries.