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Purpose -To show a possible implementation of surface impedance boundary conditions (SIBCs) in a time domain formulation based on the cell method (CM). Design/methodology/approach -The implementation is based on vector fitting (VF), a technique which allows a time domain representation of a rational approximation of the surface impedance to be found. Findings -It is shown that very little computational effort is needed to find a very good VF approximation of simple SIBCs and that such approximation is easily fitted into existing CM codes.Research limitations/implications -The extension to higher order SIBCs has not been taken into account. Practical implications -The proposed approach avoids the use of convolution integrals, is accurate and easy to implement. Originality/value -This paper introduces the use of VF for the approximate time domain representation of SIBCs.