Non-linear simulation of strain-softening materials like concrete is often impeded by the presence of singular points encountered along the equilibrium path. Singular points are mathematically defined and classified according to their physical signification. Available numerical techniques aimed at the treatment of each type of singular point are presented. Emphasis is placed on bifurcation analysis. The different nature of structural and local bifurcation is stressed. Two numerical examples of structural bifurcation are presented. In the first example, a direct tension test on a notched plain concrete bar is simulated. Two types of approach are used to tackle the ensuing symmetric bifurcation. In the second example, a non-symmetric bifurcation is analysed, simulating a direct tension test on a tapered concrete bar. The bifurcation analysis techniques introduced are shown to be effective. The need for systematic bifurcation analysis in the non-linear simulation of strain-softening materials is concluded.

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