The paper presents an alternative approach to matrix fragmentation in unidirectionally reinforced CMCs. It is based on a description of the distribution of fracture-inducing flaws using the Beta function. A flaw-strength density function is then derived using linear-fracture mechanics. This model allows prediction of the mechanical behavior from characteristics of the fibres, the matrix and the interphase. It is applied to SiC/C/SiC minicomposites tested under tension. The computed force-strain behaviour of the minicomposites is found to be in good agreement with the experimental results. It is compared to that predicted using the Aveston-Cooper-Kelly approach. Finally, the flaw densities function determined for the CVI-SiC matrix highlighted a scale effect.