[en] A method is described for calculating the surface impedance of thin superconducting films using the theory of Mattis and Bardeen of the surface impedance of superconductors. An approximate extension of the theory to the case where the superconducting order parameter inside the film varies slowly in space is presented. Calculations using the theory are compared with experimental measurements of the surface impedance at 3 GHz of thin tin films on bulk lead substrates. Agreement between theory and experiment is good