A constitutive model for fibre reinforced cementitious composites based on micromechanical solutions is presented. The model employs a two-phase composite based on the Eshel by matrix-inclusion solution and the Mori-Tanaka homogenization scheme and also simulates directional microcracking. An exterior point Eshelby based criterion is employed to model crack-initiation in the matrix-inclusion interface. Microcrack surfaces are assumed to be rough and able to regain contact under both normal and shear displacements. Once cracks start to develop, the crack-bridging action of fibres is simulated using a local constitutive equation that accounts for the debonding and pull-out of fibre groups with different orientations. It is shown that the combination of the rough microcrack and fibre-bridging sub-models allows microcracking behaviour deriving from both tensile and compressive loads to be modelled in a unified manner. Numerical results obtained with the proposed micromechanical constitutive model are compared with experimental data. Good correlation between numerical and experimental responses demonstrates the potential of the model to capture key characteristics of the mechanical behaviour of fibre reinforced cementitious composites.