A method for studying brittle fracture in an infinite plate containing interacting cracks of complex shape under general loading conditions is developed and studied for accuracy and potential applications. This technique is based on superposition and dislocation theory and can be used to determine the full stress and displacement fields in a cracked body. In addition, stress intensity factors at both crack tips and wedges, created by crack kinking and branching, are calculated so that crack growth and initiation can be analyzed at these locations of possible crack propagation. Such information can then be used to study damage accumulation in structures containing a large number of interacting cracks.