Photons penetrate the attenuating material close to the aperture of pinhole collimators in nuclear medicine, broadening the tails of point spread functions (PSFs) and degrading the resolution of planar and SPECT images. An analytic approximation has been developed that models this penetration contribution to the PSF for knife-edge point pinhole apertures. The approximation has the form exp(-gamma r), where r is the distance on the detector surface from the projection of the point source through the pinhole. The rolloff coefficient gamma is a function of the photon energy, point source location and the design parameters of the collimator. There was excellent agreement between measured values of gamma from photon transport simulations of I-131 point sources (364 keV emission only) and theoretical predictions from the analytic formula. Predicted gamma values from the analytic formula averaged 25% greater than measured values from experimental I-131 point source acquisitions. Photon transport simulations were performed that modelled the 364 keV and less abundant 637 and 723 keV emissions and scatter within the scintillation crystal. Measured gamma values from these simulations averaged 12% greater than the experimental values, indicating that about half of the error between the analytic formula and the experimental measurements was due to unmodelled 637 and 723 keV emissions. The remaining error may be due in part to scatter in the pinhole region and backscatter from gamma camera components behind the scintillation crystal. The analytic penetration model was used in designing Metz filters to compensate for penetration blur and these filters were applied to the projection data as part of 3D SPECT image reconstruction. Image resolution and contrast were improved in simulated and experimental I-131 tumour phantom studies. This analytic model of pinhole aperture penetration can be readily incorporated into iterative 3D SPECT pinhole reconstruction algorithms.