Biological tissues are made from nano-composite materials and given the recent interest in manufacturing synthetic nano-composites an analysis of natural nano-composites seems a worthwhile exercise. There is also potential for extracting natural nano-fibres and using them as reinforcements in other materials. In this paper a hierarchical mechanical model is formulated to describe potato tuber tissue and the model is used to back calculate the properties of cell wall nano-fibres. The model contains two structural levels, the cell structure and the cell wall structure. Material properties are assigned at the level of cell wall microfibrils (nano-composite fibres). Force deflection data from the compression of cubes of potato tissue were fed into the model and the properties of the cell wall microfibrils predicted. The modulus was found to vary with strain, but had a maximum value of 130 GPa, which is close to predictions from theoretical chemistry for the stiffness of cellulose microfibrils. At 8% wall strain (the value at which failures were suspected to begin), the stress was predicted to be 7.5 GPa which is also close to theoretical chemistry predictions for the strength of cellulose microfibrils. The large strains and decreasing stiffness indicate the influence of polymers other than cellulose.