We performed a combination of experiments and mechanical simulations to assess the importance of cell geometry and wall structure in tissue and cell mechanics. Osmotic treatments combined with live imaging were used to quantify deformations at the tissue, cellular, and subcellular levels. We used the adaxial epidermis of onion scale as a model system. We found that the osmotically induced surface strain in onion is small because outer periclinal walls are thick and stiff, requiring bending stiffness to be considered in our mechanical models. As expected, the mechanical behaviors of the tissue and its component cells are related. Upon changes in internal pressure, cells embedded in the tissue undergo deformation that is different from isolated cells, while the tissue undergoes a somewhat counterintuitive deformation, e.g., shrinking upon pressurization, that depends on cell geometry. At the subcellular level, the amount of deformation and its anisotropy vary within the walls of individual cells, and are affected by the cell shape and vicinity of three-way wall junctions. When the turgor pressure is lost, the protoplast-facing wall surface wrinkles due to buckling, with the pattern of wrinkles depending on the strain anisotropy and the local wall geometry.