The finding that there are considerable tissue stresses (TSs) in the hypocotyl of Helianthus annuus L. prompts the question: how are the stresses generated? Here, a one-dimensional model is formulated which, based on (i) symplastic, turgor-induced extensions of tissues which differ in moduli of elasticity, and (ii) static equilibrium, predicts the occurrence of longitudinal TSs in stem-like organs, and gives their dependence on turgor pressure. To calculate the longitudinal forces which generate the TSs in a stem, the moduli of elasticity of the tissues need to be known. The moduli were determined for uniaxial and multiaxial stresses for the outer tissue (OT) and the inner tissue (IT) of the hypocotyl. In the OT, the moduli were strongly dependent on applied uniaxial stress. The magnitudes of the calculated longitudinal forces (tensile and compressive) in the hypocotyl, were comparable to those measured. It follows that the TSs may arise without differential growth of the tissues.