A crystallographic LEED I/V characterization of thin Co/Cu(100) films is presented. Results from dynamical LEED calculations are compared with experiments via Pendry's reliability factor. The first Co layer grows with a small, but noticeable, amount of Co atoms in the second layer. For thicker films up to at least 10 ML, Co is found to grow on Cu layer by layer in a tetragonally distorted structure. The film adopts the lateral Cu spacing with an in-plane lattice expansion and a contraction of the vertical interplanar distances. By subsequent Cu on Co deposition, lateral and vertical Cu spacings are kept, reproducing the initial substrate structure.