A regression model composed of two sigmoid functions with variable asymptotes was developed and used to analyse the dietary fibre supplement behaviour during bread dough mixing. Using eight commercial dietary fibres of different botanical origin and model wheat starch-gluten flour, farinograph curves for fibre-flour blends and for the flour only were performed. After smoothing of the curves with the regression model, difference farinograms as the fibre supplementation effects were determined. The results showed that the difference farinograms had two peaks, whose shape was strongly differentiated by the studied supplements. The presence of both peaks allowed distinguishing two kinds of the rheological activity of each fibre supplement: weakening and strengthening of the consistency of bread dough during its development. The carrot, oat, cranberry, and cacao fibres exhibited dominance of strengthening over weakening action. While chokeberry, carob, apple, and flax fibres were characterised by dominance of weakening over strengthening action. The analysis of both position and height of the peaks in the difference farinogram can be also helpful for determination of hydration kinetics of the fibres used for bread supplementation.