The application of analytical methods to the problem of fatigue crack propagation and branching is complicated by the shortage of information on the stress distribution near the tip of cracks of complex configuration. A discussion of this problem and a survey of the studies in this area can be found in [1], for example. Below we develop a method of solving a problem concerning a system of cracks of complex form in an anisotropic half-plane. An efficient algorithm for numerical solution of the problem is proposed. A study is made of the effect of anisotropy of the material, the free edge of the plate, and the curvature of the crack on the stress intensity factors at the tips of the cracks.