On the other hand the extensive use of brittle matrix composite materials requires appropriate computational models to describe, with adequate accuracy, their mechanical behaviour. In the present paper a mechanical-based computational model for the description of the macroscopic behaviour of such a class of materials, composed by a matrix phase and a fibre-reinforcing phase, is formulated. By considering a micromechanical-based model, the macro constitutive equations of unidirectional or randomly distributed fibres reinforced materials are obtained by taking into account the possibility of crack formation and propagation in the matrix as well as fibre debonding and breaking. The developed computational model is finally used in some numerical simulations in order to outline its reliability in the assessment of both the fibre-matrix interaction phenomenon as well as the fracture failure prediction capability in brittle matrix FRC materials.