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a b s t r a c tIn this paper, we present a fracture model for composite laminates and its numerical solution by using the Fast Fourier Transforms (FFTs). The FFT-based formulation initially proposed for seeking the average behaviour of linear and non-linear composites by means of the homogenisation procedures [1,2] was adapted to evaluate the damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed to assess the failure in the matrix and the fibres. This non-local model was then connected to the Griffith-Irwin criterion in the aim of predicting crack growth. In order to assess the matrix/fibre interface delamination, we have adapted the cohesive model developed by Li [3] for accounting the mixed-mode dependent interface failure. To this end, the interfaces between the matrix and the fibres are replaced by a thin layer of interphase with the purpose of facilitating the FFT simulations. By using the proposed model, we carried out several numerical simulations on fracture process in different specimens. From these studies, we can conclude that the present FFTbased analysis is capable to deal with crack initiation and crack growth in composite laminates with high accuracy and efficiency, especially in the cases of matrix/fibre interface debonding and of multi-crack growth.