The thesis describes the development of a new continuum damage mechanics (hereafter, CDM) model for the deformation and failure of brittle matrix composites reinforced with continuous fibres. The CDM model is valid over sizes scales large compared to the spacing of the fibres and the dimensions of the damage. The composite is allowed to sustain damage in the form of matrix micro-cracking, shear delamination, tensile delamination and fibre failure. The constitutive equations are developed by decomposing the composite compliance into terms attributable to the fibre and matrix, and modelling the competing failure modes by intersecting failure surfaces based on maximum stress theory. The fibres are treated as being weakly bonded to the matrix so that the fibres only transmit axial loads, and fail in tension. The matrix is modelled as isotropic linear elastic and is treated as transversely-isotropic after damage has initiated. The effect of multiple matrix cracking on the stiffness was determined from experimental data, while failure was modelled by a rapid decay in the load bearing capacity. Although the model is motivated largely to proportional loading, matrix unloading and damage closure has been modelled by damage elasticity. During compression, the matrix stiffness is identical to the undamaged state with the exception that the fibres are assumed not to transmit compressive loads. The model was implemented computationally through a FORTRAN subroutine interfaced with the ABAQUS/Standard finite element solver. The CDM model was validated by comparing experimental and computational results of test specimens with unidirectional and balanced 0°-90° woven fibres of a brittle matrix composite, fabricated from polyester fibres in a polyester matrix. This composite system exhibits low elastic mismatch between fibres and matrix, and has similar non-dimensionalised stress-strain response to a SiC/SiC composite proposed for the exhaust diffuser unit of the Rolls-Royce EJ200 aero-engine.