This study examined the magnetic properties of ultrathin Fe/Ni films on a Cu(001) surface using the full potential linearized augmented plane wave (FLAPW) method. The magnetic moment of Fe/Ni films was found to be insensitive to strain. Nevertheless, strain had a significant influence on the magnetization direction. For example, Fe/Ni films showed a thickness-dependent spin reorientation transition in the presence of strain, while the Fe/Ni films grown pseudomorphically on Cu(001) always showed perpendicular magnetization. In addition, the theoretically calculated X-ray magnetic circular dichroism (XMCD) was examined.