Non-linear simulation of strain-softening materials is often impeded by the presence of singular points encountered along the equilibrium path. Available numerical techniques aimed at the treatment of singular points are presented. Emphasis is placed on bifurcation analysis. Two numerical examples of structural bifurcation are presented. In the first example, a direct tension test on a notched concrete bar is simulated, displaying a symmetric bifurcation. In the second example, a direct tension test on a tapered concrete bar is simulated, displaying a non-symmetric bifurcation. 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.