Morphogenesis in plants occurs as a combined outcome of hormone pattern formation and mechanical changes involving cell growth and division. In this work a method was developed for measuring mechanical properties of plant cells at sub-cellular resolution using the atomic force microscope. Initial work focussed on the measurement of the mechanical properties of a number of wild type and transgenic Arabidopsis hypocotyls. Mutants in expansin expression were measured and were hypothesised to have cell walls of reduced stiffness. Due to the variation in results, or the wrong hypothesis, trends that fitted with the hypotheses were not seen. A series of experiments were performed to investigate this variance and standardise future measurements. An investigation into the effect of angle of indentation and depth of indentation were carried out. Following on from this work focussed on the stomata. A series of experiments were carried out to quantify the mechanical properties of these cells, comparing them to the properties of the cells surrounding them. Multivariate correlation analysis was performed to test hypotheses that these measurements correlated with other geometrical parameters, such as how open the stomate is and how large it is and significant correlations between these were found. A model of auxin pattern formation in the leaf margin was developed that incorporated knowledge of a family of auxin importers thought to have an important role in morphogenesis. These results show that auxin importers may have a role in stabilising the patterning of hormones and influence the timing and positioning of hormone peaks. This model highlighted the fact that the idea of a cell’s sensitivity to auxin is important and may have an affect when considering how auxin effects the growth of cells.