Guard cells dynamically adjust their shape to regulate photosynthetic gas exchange, respiration rates and defend against pathogen entry. Cell shape changes are determined by the interplay of cell wall material properties and turgor pressure. To investigate this relationship between turgor pressure, cell wall properties and cell shape, we focused on kidney-shaped stomata and developed a biomechanical model of a guard cell pair. Treating the cell wall as a composite of the pectin-rich cell wall matrix embedded with cellulose microfibrils, we show that strong, circumferentially-oriented fibres are critical for opening. We find that opening dynamics are dictated by the mechanical stress-response of the cell wall matrix, and as the turgor rises, the pectinaceous matrix stiffens. We validate these predictions with stomatal opening experiments in selected Arabidopsis cell wall mutants. Thus, using a computational framework that combines a 3D biomechanical model with parameter optimisation we demonstrate how to exploit subtle shape changes to infer cell wall material properties. Our findings reveal that proper stomatal dynamics builds on two key properties of the cell wall, namely anisotropy in the form of hoop reinforcement and strain-stiffening. This article is protected by copyright. All rights reserved.