We present CanSPART: a model of gap probability (Pgap) based on a simple but flexible geometric vegetation canopy structure, coupled to a one-dimensional radiative transfer scheme, to account for the effects of crown structure and trunks on vertically resolved canopy radiation fluxes. The Pgap component of the model is intended for use in inverting ground-based and airborne gap-frequency data for biometric variables, while the full CanSPART model is intended for application within a one-dimensional multilayer soil-vegetation-atmosphere-transfer model. Our approach to modelling Pgap is novel because it uses an analytic approximation to the crown porosity, which makes it computationally efficient. Further, it can accommodate any distribution of crown and trunk heights and dimensions, allowing the model to be applied to complex canopy structures with multiple layers. The Pgap model is readily rewritten in terms of a clumping factor as a function of height and angle. Simulations of Pgap(θ,z) for idealised canopies compared favourably with those of two other models: the Analytical Clumped Two-Stream (ACTS) model (Ni-Meister et al., 2010) and an adaptation of the Nilson (1999) model. We test the analytic approximation to the crown porosity, also inherent in the Nilson (1999) model, and the applicability of a single clumping factor without angle nor height dependence. Both simplifications are demonstrated to be valid. Lovell et al. (2012, this issue) provide quantitative assessment of the Pgap component of CanSPART against ground-based lidar measurements from sites spanning a range of canopy structures.