Resins are plant exudates of economic importance used by plants as defence. They flow out of resin ducts, open and long tube-like intercellular spaces lined by a layer of specialized parenchyma cells, called the epithelium, which secrete resin into the duct lumen. A model that describes resin flow in conifers is presented to investigate how duct structure, resin loading, crystallisation, and viscosity affect flow and could explain differences between species. Considering resin viscosity, the structure of resin ducts, and a pressure-driven resin loading through the duct wall, the unsteady Stokes equation was applied. There is an increase in flow towards the open end that is favoured by the duct geometry. Both flow and pressure depend on the loading mechanism and on the duct resistance, which depends on the duct geometry, viscosity and duct wall permeability to resin. These results confirm previous measurements and observations made on Pinaceae and seem to be physiologically advantageous for the defence role of resin. Understanding of how these physiological and morphological parameters affect resin flow might be useful for selecting varieties and species having a high resin yielding capacity. The model presented in this paper is also applicable to other external secretory systems in plants.