With the development of material science, especially as MEMS/NEMS are playing a more and more important role in modern engineering, some mechanical behaviors of materials, e.g., fracture, shear instability, need to be investigated from multidisciplinary perspective. The molecular dynamics (MD) simulations are performed on single-crystal copper block under simple shear to investigate the size and strain rate effects on the mechanical responses of face-centered cubic (fcc) metals. It is shown that the yield stress decreases with the specimen size and increases with the strain rate. Based on the theory of dislocation nucleation, a modified power law is proposed to predict the scaling behavior of fcc metals. In the MD simulations with different strain rates, a critical strain rate exists for each single-crystal copper block of given size, below which the yield stress is nearly insensitive to the strain rate. A hyper-surface is therefore formulated to describe the combined size and strain rate effects on the plastic yield stress of fcc metals.