A fracture model based on two-dimensional plane stress-strain elasticity theory is developed for the problem of periodic, interacting and regularly spaced matrix cracks in a unidirectional fiber-reinforced brittle matrix composite. The solution is obtained in terms of a hypersingular integral equation. The effects of the fiber reinforcement, and the spacing, the location and the length of cracks on the stress intensity factors at the crack tips and the maximum crack opening displacement in the composite are studied.