The perpendicular magnetic anisotropy (PMA) properties of CoFeB/Pd multilayers are investigated as functions of the thickness of the constituent layers of the multilayers and of the substrate type. A relatively strong PMA is formed at small CoFeB thicknesses of 0.3 and 0.5 nm over the entire Pd thickness range of 0.47 to 1.26 nm. At a fixed CoFeB thickness, the PMA tends to increase with increasing Pd thickness and this behavior can be attributed to the fact that the interface tends to become flatter and smoother at a higher Pd thicknesss, leading to a stronger surface anisotropy. A stronger PMA is observed for the glass substrate than for the MgO substrate. Since the thermal stress formed at the CoFeB layer is tensile for both the glass and MgO substrates, the magnetoelastic interactions suggest the possibility of forming a Co-Pd alloy with a negative saturation magnetostriction at the CoFeB/Pd interfaces.