The present paper deals with the problem of modelling the complete macroscopic response of short fibre reinforced cementitious composites under unidirectional tensile loading. It is considered a concrete matrix with a periodic distribution of cracks and fibres. A cell model is used to represent the periodic microstructure and the overall properties of the composite are de_ned using the homogenization theory for material with periodic microstructure. The damage of the FRC is modeled considering the evolution of a process zone and a propagation of an initial crack, taking into account the bridging action of the bers. A new numerical procedure is developed to evaluate the nonlinear response of the material. In particular, the softening process is investigated studying a simple nonlinear algebraic equation, whose coe_cients are evaluated solving linear elastic problems. A numerical application is developed to determine the overall behavior of FRC, and to assess the proposed numerical procedure.