The counterflow virtual impactor (CVI) samples droplets larger than a certain size by inertially separating them from the surrounding air and small aerosol particles. Previous studies of this instrument were of an experimental character. Here we present a mathematical model of the CVI. The flow field is simulated by a three-dimensional axis-symmetrical potential dow model. The particle trajectories and the CVI collection efficiency are calculated. Finally, the model is applied to a calibrated CVI (Anderson et al., 1993, Aerosol Sci. Technol. 19, 317-329). The modelling results are in good agreement with the experimental data.