Room-temperature perpendicular magnetic anisotropy (PMA) was observed in Ni/Pt multilayer films having 7-30 Angstrom Ni and constant 3 Angstrom Pt sublayer thickness, prepared by magnetron sputtering at an Ar sputtering pressure of 7 mTorr. To understand the origin of PMA, the magnetoelastic anisotropy was determined from delicate in situ stress and ex situ magnetostriction coefficient measurements. Tensile stress, inversely decreased with the Ni sublayer thickness, was observed in all samples prepared at this sputtering pressure while the magnetostriction coefficient was found to be negatively increased as the Ni sublayer thickness increased. From the measurements of stress and magnetostriction coefficient, we have found the magnetoelastic anisotropy of 2.88-4.72x10(5) erg/cm(3) in the samples, which was large enough to overcome negative contributions from the surface and shape anisotropies. Thus, it could be concluded that the magnetoelastic anisotropy plays a major role in yielding PMA in this system. [S0163-1829(99)50110-0].