The concept of detecting symmetry within 3D models has received an extensive amount of research within the past decade. Numerous algorithms have been proposed to identify reflective symmetry within 3D meshes and to extract a quantitative measure for the model’s level of symmetry. Much of this existing work focuses on identifying symmetry in noiseless 3D models with most methods unable to work effectively on models distorted by noise, such as those commonly obtained when scanning objects in the real world. This report details the design and implementation of two robust and fast algorithms, which can be used on a wide variety of models to identify global approximate reflective symmetry. These proposed methods are also able to identify likely planes of symmetry in models that have been distorted with noise or contain minor imperfections, making them ideal for scanned models of real world objects. The hypothesis planes are determined by principal component analysis, after which the proposed algorithms give each plane a numerical value corresponding to its likelihood of being a plane of global approximate reflective symmetry. The first algorithm uses the Hausdorff distance between vertices to estimate symmetry, whilst the second uses an approach based on ray casting. We estimate the accuracy of our proposed methods to be 96.88% for the Hausdorff distance method and 93.75% for the ray casting method.