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To understand and develop new nanostructure materials with specific mechanical properties,a good knowledge of the elastic strain response is mandatory.Here we investigate the linear elasticity response in the modified phase-field-crystal (MPFC) model.The results show that two different propagation modes control the elastic interaction length and time,which determine whether the density waves can propagate or not.By quantitatively calculating the strain field,we find that the strain distribution is indeed extremely uniform in case of elasticity.Further,we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus.The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.