Abstract: A new strain gradient theory based on energy non-localmodel is proposed in the paper, and applied to predict the micro-indentationhardness of polycrystalline copper and the thin film--substrate system.First, an energy non-local model is presented to derive the constitutiveequation of a new strain gradient theory. Second, the finite element formulaof the new strain gradient theory is obtained with the case of theprediction of micro-indentation hardness. It is found that the predictedresults by the new strain gradient theory agree well with the experimentaldata, while the hardness values predicted by classic plasticity theory areremarkably lower than the experimental data.