Interactions of incident photons with the collimator and detector, including septal penetration, scatter and x-ray fluorescence, are significant sources of image degradation in applications of SPECT including dual isotope imaging and imaging using radioisotopes that emit high- or medium-energy photons. Modelling these interactions using full Monte Carlo (MC) simulations is computationally very demanding. We present a new method based on the use of angular response functions (ARFs). The ARF is a function of the incident photon's direction and energy and represents the probability that a photon will either interact with or pass through the collimator, and be detected at the intersection of the photon's direction vector and the detection plane in an energy window of interest. The ARFs were pre-computed using full MC simulations of point sources that include propagation through the collimator–detector system. We have implemented the ARF method for use in conjunction with the SimSET/PHG MC code to provide fast modelling of both interactions in the patient and in the collimator–detector system. Validation results in the three cases studied show that there was good agreement between the projections generated using the ARF method and those from previously validated full MC simulations, but with hundred to thousand fold reductions in simulation time.