The ability to identify and quantify asymmetrical shape change is potentially valuable in the study of biological shapes. This thesis describes a new approach to the analysis of symmetry in two dimensional shapes. Two methods of quantifying asymmetry and a means of identifying the boundary distortions that cause them are posited. Underlying these techniques is the assertion that symmetry is a continuous, measurable property of shape, encapsulated in a detectable curve equivalent to the bilateral axis. Theories from psychology and computer vision are used to justify these claims and a unique combination of image analysis techniques is used in the practical execution of these ideas. Central to the implementation of this new approach to symmetry analysis is the ability to isolate and extract the bilateral axis. A novel approach to axis identification is developed that involves the interrogation of the local symmetries in each boundary in a multi-scale description of a shape using active contours. A set of nine test shapes that exhibit a wide variety of asymmetry is used to demonstrate the operation and effectiveness of this technique.