Modelling the ductile performance of concrete structures, particularly for fail-safe and earthquake situations, is still unsatisfactory owing to a cumbersome description of material behaviour. This paper reviews the development of concrete failure criteria and, arising from the distinction between the stress–strain relations measured in tests and ‘independent' material performance, identifies the previously suggested criterion of limiting tensile strain as the most promising for behaviour prediction especially in finite-element exercises. The full description of this single-parameter criterion in the three-dimensional space of principal stress is provided. Its use conveniently avoids the numerical difficulties involved in the hypoelastic material behaviour modelling of current practice and its validity becomes very clear when used to interpret the results of previous experimental work and when compared with other theories.