This paper aims to get insight into the physical significance of the results obtained from curve fitting of a stochastic cracking model on experimental tensile stress-strain data of cementitious composites which are uniaxially reinforced with continuous fibre bundles of different kinds, such as glass, basalt, carbon, polyethylene and polyvinyl alcohol fibres. An experimental test program is performed on the different composites containing typically 20% in volume of fibres, as well on the fibre bundles themselves. A short introduction is given to the theory behind the stochastic cracking model, based on a Weibull distribution of the matrix cracking stress, which is used for modelling the experimental results. The obtained tensile stress–strain curves are analysed by means of curve fitting and an attempt is made to draw conclusions on the physical meaning of these results. The experimental results of tensile tests on specimens with an inorganic phosphate cement matrix containing the different fibre types, revealed a wide range of mechanical behaviour: carbon fibres result in a very stiff material, PE fibres in a very strong material, while the use of PVA fibres results in a very flexible and ductile composite. Curve fitting of the stochastic cracking model on the experimental data was successfully performed, leading to the identification of the Weibull model parameters. The reference cracking strength was found to be much higher than the mean matrix cracking strength. An interpretation, based on the phenomenon of crack suppression, is given for these high values compared to those found in literature for cement composites.