Perpendicular magnetic anisotropy(PMA) at room temperature in Ni/Pt multilayer thin films was obtained for samples of constant 3 Angstrom Pt and 7-16 Angstrom Ni sublayer thicknesses, prepared by sequential de magnetron sputter deposition. Accurate stress and magnetostriction measurements revealed that stress-induced magnetoelastic anisotropy was a major origin for the observed PMA in this system.