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Relation between the elastic modulus and the diameter (D) of ZnOnanowires was elucidated using a model with the calculated ZnOsurface stresses as input. We predict for ZnOnanowires due to surface stress effect: (1) when D>20nm, the elastic modulus would be lower than the bulk modulus and decrease with the decreasing diameter, (2) when 20nm>D>2nm, the nanowires with a longer length and a wurtzite crystal structure could be mechanically unstable, and (3) when D<2nm, the elastic modulus would be higher than that of the bulk value and increase with a decrease in nanowire diameter.