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In a dynamic unbounded medium–structure interaction analysis in the time domain performed with the substructure method the unit-impulse response function on the structure–medium interface of the unbounded medium is determined. The consistent infinitesimal finite element cell method based solely on the finite element formulation has been developed for compressible elasticity. In this paper the procedure is expanded to the incompressible case. The limit of Poisson's ratio =0·5 is performed analytically. This yields a concentrated mass in the formulation representing the instantaneous response over the entire domain not present in compressible elasticity. The only modification appears in the coefficient matrices of the consistent infinitesimal finite element equation which can be solved with the same numerical algorithm as in the compressible case. Excellent accuracy results also in very complicated inhomogeneous situations. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]