We present a surrogate model for the elastic–plastic response of an aluminium alloy, based on simple neural networks trained on measurements taken in tension–torsion and compression-torsion experiments. In these tests hollow cylindrical test specimens are subjected to pseudo-random time histories of applied axial force and torque. Multiple random experiments are conducted to explore the strain and stress space in both the elastic and elastic–plastic regimes of material behaviour. The corresponding histories of axial and shear stress and strain are subdivided in small increments, each of which representing a unit training datapoint. A surrogate model in strain control, based on feed-forward neural networks, is implemented; this comprises a classification network, which distinguishes elastic from elastic-plastic increments, and a regression network to compute the increment in stress as a function of the increment in total strain. The accuracy of the model is evaluated by predicting the material’s response to random loading histories not included in the training dataset.