An analytical method for studying brittle fracture in an infinite plate containing a crack of complex geometry under general loading conditions is developed. Based on superposition and dislocation theory, this method can be used to determine the full stress and displacement fields in a cracked material. In addition, stress singularities at both crack tips and material wedges (created by crack kinking or zigzagging) are calculated. A key component of this research is the development of opening displacement series that capture the physical behavior of the cracks. Cracks with multiple kinks (or changes in growth direction) are studied with this method. Results show rapid convergence for few degrees of freedom as measured by the number of opening displacement terms included in a particular analysis.