AbstractTwo equivalent semi‐discrete formulations are presented for the problem of the transient response of soil‐structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non‐linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately.The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free‐field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil‐structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil‐structure interface of the complete system. It is shown, further, that the free‐field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free‐field ground motion at a site is usually specified at a single