A crystal plasticity finite element constitutive model combined with Bassani and Wu hardening law has been developed to investigate the effects of grain/phase boundary (GB/PB) on mechanical properties and microtexture evolution of Cu bicrystals and Cu–Al bicrystals during nanoindentation process. The simulated load–displacement curve for the Cu single crystal with Goss initial orientation has been analyzed and compared with the result from the experiment to validate the parameters. The numerical results indicate that the effects of GB/PB on load–displacement curves, indentation Young's moduli, Mises stresses, pile-up patterns are insignificant for Cu bicrystals while they are significant for Cu–Al bicrystals. The main reason is that PB works as a very effective barrier to resist the plastic slip propagation of the deformed material. The effects from different misorientations of GBs/PBs are insignificant for both Cu bicrystals and Cu–Al bicrystals. The effects of GB/PB on lattice rotation angles for both Cu bicrystals and Cu–Al bicrystals are significant.