Magnetic anisotropy depends strongly on the density of states at the Fermi level. If significant contributions to magnetocrystalline anisotropy energy (MAE) are due to spin-polarized quantum well states (QWS), a significant increase of MAE can occur periodically as a function of film thickness. The oscillation period L is determined by the wavelength of the corresponding electron waves. The uniaxial magnetic anisotropy of fcc-Co is found to oscillate with a period of 2.3 ML. In contrast, in bcc-Fe, the uniaxial magnetic anisotropy oscillates with a period of 5.9 ML. We attribute such oscillations to QWS in a minority-spin d-band at the Fermi level.