Multicellular organisms grow and acquire their shapes by controlling the differential expansion and deformations of their cells. Recent research has addressed the role of the mechanical properties of cells and tissues in these processes. In the case of plants, it is generally believed that growth rate is a function of the mechanical stress exerted on the cell wall, the thin polymeric layer surrounding cells, involving an effective viscosity. Nevertheless, recent work has pointed to the relevance of cell wall elasticity in setting growth rate. To extensively assess this relevance, we chose to work on the genetically identical small plants produced in Marchantia polymorpha and we developed a microfluidic device to study the early growth and elastic properties of individual plants in a controlled environment with a high-throughput. We characterized the effect of osmotic treatment and of abscisic acid on plant growth and mechanics. Overall, we show that the instantaneous growth rate of individuals is significantly correlated to their bulk elastic modulus, with a correlation coefficient that changes with treatments. Our results are consistent with a framework in which growth rate is determined by elasticity of the wall and a chemical rate associated with remodeling of the cell wall or with changes in its composition. Accordingly, we propose that a tight coupling between mechanics and chemistry of the cell wall is key to setting growth patterns during morphogenesis.