We have studied the structures formed by the deposition of 0.5 and 1 monolayer (ML) of Pd on a Cu(001) surface using Monte Carlo (MC) simulations and static optimizations. The energetics are given by the semiempirical embedded atom method (EAM). At 0.5 ML Pd coverage we find that a Pd–Cu c (2×2) single layer surface alloy is created, consistent with experimental observations. At 1 ML Pd coverage a double layer c (2×2) Cu–Pd surface alloy is found to be energetically favored over structures with a clock-reconstructed topmost layer. However, metastable configurations of the top layer consisting of a clock-rotated phase with the (2×2) p4g symmetry coexisting with phases with c (2×2) and p (2×2) symmetries can also be obtained, in agreement with the experimental results.