The intertwining between mechanics and developmental biology is extensively studied at the shoot apical meristem of land plants. Indeed, plant morphogenesis heavily relies on mechanics; tissue deformations are fueled by turgor-induced forces, and cell mechanosensitivity plays a major regulatory role in this dynamics. Since measurements of forces in growing meristems are still out of reach, our current knowledge relies mainly on theoretical and numerical models. So far, these modeling efforts have been mostly focusing on the epidermis, where aerial organs are initiated. In many models, the epidermis is assimilated to its outermost cell walls and described as a thin continuous shell under pressure, thereby neglecting the inner walls. There is, however, growing experimental evidence suggesting a significant mechanical role of these inner walls. The aim of this work is to investigate the influence of inner walls on the mechanical homeostasis of meristematic tissues. To this end, we simulated numerically the effect of turgor-induced loading, both in realistic flower buds and in more abstract structures. These simulations were performed using finite element meshes with subcellular resolution. Our analysis sheds light on the mechanics of growing plants by revealing the strong influence of inner walls on the epidermis mechanical stress pattern especially in negatively curved regions. Our simulations also display some strong and unsuspected features, such as a correlation between stress intensity and cell size, as well as differential response to loading between epidermal and inner cells. Finally, we monitored the time evolution of the mechanical stresses felt by each cell and its descendants during the early steps of flower morphogenesis.