AbstractIn a bounded domain elasto‐plastic wave propagation can be modelled accurately using the finite‐element method. As is even the case for an elastic analysis, an unbounded domain, e.g. a semi‐infinite soil or fluid, can, however, not be represented in this manner, as any spatial discretization has to be avoided. For one‐dimensional wave propagation with a bi‐linear elasto‐plastic material law involving one stress component an analytical solution exists. The latter is used in modelling the non‐linear far field of an unbounded medium using a rigorous bookkeeping procedure of the generated elastic and plastic waves propagating in both directions. The need for a non‐linear model of the far field arises, as in a two‐dimensional representation of soil‐structure interaction the surface