The oil palm (Elaeis guineensis Jacq.) maintains a large leaf area throughout the year, but its productivity is limited by a low rate of dry matter production per unit leaf area. Stomatal closure, at times of low soil water availability and high atmospheric vapour pressure deficit, is an important factor limiting photosynthesis and hence dry matter production. In this paper, laboratory and field data are used to prepare a model of the relationships between net photosynthetic rate and stomatal conductance, and between stomatal conductance and environmental variables. Results show that high atmospheric vapour pressure deficits may limit production even in parts of the world where oil palms are not normally considered to suffer from water stress. The model can be used to design and evaluate irrigation systems, and to help quantify the potential value of oil palm genotypes with low stomatal sensitivity to either VPD or available soil water for use where irrigation is impractical.