The fracture problem of laminated plates which consist of bonded orthotropic layers is studied. It is assumed that the medium contains periodic cracks normal to the bi-material interfaces and the external loads are applied away from the crack region. The field equations for an elastic orthotropic body are transformed to give the displacement and stress expressions for each layer or strip. The unknown functions in these expressions are found by satisfying the remaining boundary and continuity conditions. A system of singular integral equations is obtained from the mixed boundary conditions. Three cases are considered: (a) The case of internal cracks; (b) The case of broken laminates; and (c) The case of a crack crossing the interface. The singular behavior around the crack tip and at the bi-material interface is studied. It is shown that the crack surface displacement derivative has a power singularity for practical orthotropic materials when the crack touches the interface, i.e., for case (b). In studying the singular behavior at the bimaterial interfaces in case (c ), it is found that for some orthotropic material combinations there is no singularity in the crack surface displacement derivatives and the stresses.