A geometric model and calibration process are developed for single photon emission computed tomography (SPECT) imaging with multiple pinholes and multiple mechanical axes. Unlike the typical situation where pinhole collimators are mounted directly to rotating gamma ray detectors, this geometric model allows for independent rotation of the detectors and pinholes, for the case where the pinhole collimator is physically detached from the detectors. This geometric model is applied to a prototype small animal SPECT device with a total of 22 pinholes and which uses dual clinical SPECT detectors. All free parameters in the model are estimated from a calibration scan of point sources and without the need for a precision point source phantom. For a full calibration of this device, a scan of four point sources with 360 degrees rotation is suitable for estimating all 95 free parameters of the geometric model. After a full calibration, a rapid calibration scan of two point sources with 180 degrees rotation is suitable for estimating the subset of 22 parameters associated with repositioning the collimation device relative to the detectors. The high accuracy of the calibration process is validated experimentally. Residual differences between predicted and measured coordinates are normally distributed with 0.8 mm full width at half maximum and are estimated to contribute 0.12 mm root mean square to the reconstructed spatial resolution. Since this error is small compared to other contributions arising from the pinhole diameter and the detector, the accuracy of the calibration is sufficient for high resolution small animal SPECT imaging.