A fracture model based on two dimensional plane stress/strain elasticity theory for the problem of doubly periodic interacting and regularly spaced matrix cracks in a unidirectional fiber reinforced brittle matrix composite is developed. The solution is obtained in terms of a singular integral equation. The stress intensity factors at the crack tips, the maximum crack opening displacement and the longitudinal stiffness of the composite are studied as a function of the elastic moduli of the constituents, fiber volume fraction, transverse crack spacing, and crack length. The crack spacing is found to be more dominant than the relative constituent stiffness properties and the fiber volume fraction in influencing the stress intensity factor and the crack opening displacements. The stiffness of the composite due to multiple cracking reduces with a decrease in the fiber crack spacing. The stress intensity factors from the current planar model are compared with the axisymmetric results available in the literature and show a considerable difference between the results.