Cellular growth is ultimately a biomechanical process. In plants, the major biomechanical forces are the cellular pressure, or “turgor pressure”, and the resulting cell wall tension. Specifically, osmosis causes cellular pressure build-up and stretches the cell walls to expand, leading to many biophysicists comparing plant cells to “water-filled balloons”. Despite this analogy, the precise role of tissue hydraulics in plant meristematic tissues remains elusive. Here, by combining nanoindentation measurement, 4D confocal live imaging and physical modelling, we demonstrate that cellular pressure is highly heterogeneous within the shoot apical meristem (SAM) of the model plant Arabidopsis thaliana. We further suggest that the coupling of tissue mechanics and osmosis can predict various growth modes that cannot be recapitulated by previous models. Together, our results reveal cell pressure as a source of patterned heterogeneity and illustrate links between tissue geometry, mechanics, and growth, with potential roles in tissue homeostasis and morphogenesis.