The structural properties, elastic properties, and the heat of formations for the high entropy alloys (HEAs) AlCoCrCuxFeNi were studied by density functional theory and plane-wave pseudopotental technique with generalized gradient approximation (GGA), the crystal structure was built with the Virtual Crystal Approximation (VCA). The calculated results indicate that the mass density of HEA AlCoCrCuxFeNi increases with the increasing mole fraction of Cu, the lattice parameter is the largest when the mole fraction of Cu is 1.5. The mechanical stability of the HEA AlCoCrCuxFeNi is nothing to do with the mole fraction of Cu. The heat of formation decreases with the increasing mole fraction of Cu, but the HEAs AlCoCrCuxFeNi are thermodynamically stable due to their negative heats of formation.