Previous experimental investigations (Hirakata et al. Int J Fract 145:261-271, 2007) have demonstrated that Si/Cu/SiN/Pt/C nano-cantilever is delaminated along the interface between Cu and Si layers when subjected to monotonically bending load, and the measured load-displacement relationship shows a nonlinear behavior. Based on the continuum mechanics model, this study carries out numerical simulations on the crack nucleation and propagation along the Si/Cu interface in order to clarify the effect of plasticity on the fracture behavior of the ductile nano-component. Exponential type of cohesive zone model (CZM) combined with finite element method was adopted to characterize the constitutive relationship of the Si/Cu interface. Two sets of simulations are performed, i.e., Cu layer obeys either linear elastic or Ramberg-Osgood elasto-plastic constitutive relation. The characteristic parameters of interfacial adhesion are extracted through calibration via experimental results. The simulation results indicate that (i) cohesive strength and work of separation are the dominating CZM parameters, and the exponential CZM is suitable for describing the interfacial delamination between the Cu and Si film layers; (ii) the Cu film layer in this nano-cantilever more favorably obeys a linear elastic constitutive relation; (iii) comparing to bulk Cu, nano-scale Cu has a much higher yield stress and hardening rate, which leads to little plastic deformation of the nano-cantilever specimen during the entire delamination process. The numerical predictions are in good agreement with the experimental results, wherein brittle fracture occurred during the Si/Cu interfacial delamination. And the nonlinear load-displacement behavior observed by the tests may be due to the cohesive law of the Si/Cu interface, instead of the plastic deformation of the Cu film layer.