The rheological properties of the cell walls of soft plant tissue have a strong bearing on the stress‐strain response of the whole tissue. In this study the parenchyma cells of apple and potato tissue were osmotically manipulated in mannitol solutions, and the cell wall stress‐strain relation was inferred from precise measurements of the change in dimensions of the tissue samples. Cell wall tension was estimated from the water potential of the solutions, cell water relations, and simple shell theory. Cell wall stress versus strain showed an increasing slope with increased strain, but for potato parenchyma, slope decreased when strain exceeded 8%. Samples prestressed at high turgor showed significant irreversible deformation on subsequent plasmolysis. Two new constitutive laws were developed to describe the elastic‐plastic behavior of the cell walls.