The mechanics of fibre-reinforced concrete under uniaxial loading has been studied, the main part of the study considering the behaviour after cracking. A new constitutive model has been developed, which takes into account the strain-softening part of the stress/strain curve. In addition, the crack spacing and the crack width are calculated. The fibres are smooth and flexible. They can be short or continuous, aligned or randomly distributed, brittle or ductile, hard or soft. Moreover, different types of fibre may lie in the same matrix. The model takes into account single-fracture or multiple-cracking states and the different fracture mechanisms of fibre fracture and pull-out. The results of the new model are promising. The effects of different parameters can be studied and new formulas found, thus enabling the model to be used in the design of composite materials.