In this study, five epitaxial [Co(t nm)/Pt(1 nm)]30 multilayer samples (t=0.16-1.07 nm) were studied using polarized X-ray absorption spectroscopy method. These samples were prepared on Mo(110)/ Al2O3(11-20) substrates by MBE technique. The results show that the Co layer is more like an fcc pseudomorphic structure for the Co thickness of less than 0.3 nm. For Co layer thickness of 1 nm, the first shell distance is 0.25 nm, which is very close to the Co-Co distance of bulk hcp Co. On the other hand, for Co layer of less than 0.3 nm, the in plane first shell distance is expanded by 4% and most of the neighboring atoms are Pt atoms. The fitting results of the Co/Pt multilayers seem to support a sharp boundary model rather than an interdiffusion model.