In the present research, a systematical study of trans-scale mechanics theory is performed. The surface/interface energy density varying with material deformation is considered, and the general surface/interface elastic constitutive equations are derived. New methods to determine the material length scale parameter and the surface elastic parameters based on a simple quasi-continuum method, i.e. the Cauchy–Born rule, are developed and applied to typical fcc metals. In the present research, the material length parameters will be determined through an equivalent condition of the strain energy density calculated by adopting the strain gradient theory and by adopting the Cauchy–Born rule, respectively. Based on the surface constitutive equations obtained in the present research, the surface elastic parameters are calculated by using the Gibbs definition of surface energy density and the Cauchy–Born rule method.