Complex analysis is employed for solving crack problems in orthotropic plate materials. The governing, equations of the problem, are formulated in terms of two complex stress functions. Then, the problem is reduced to a pair of Riemann - Hilbert problems, that are solved for arbitrary stress distribution along crack surfaces. The validity of the obtained solution is proved. Then, the influences of the elastical and geometrical characteristics of the plate on values of the stress intensity factors, (KI and KII), are explained.