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Quantification of the change in shape of a residual limb over time is relevant to the fitting of an external prosthesis. Three algorithms were developed and evaluated to align residual limb shapes: iterative closest points (ICP), mean absolute difference, and weighted surface normals/mean absolute difference. Evaluations were conducted by aligning residual limb shapes with known deformations and transformations with their original shapes. Results showed that ICP did not perform well in that it tended to favor a global distribution of local shape difference rather than localization of the error. The mean absolute difference algorithm performed well as long as the shape difference was localized to one region. Weighted mean surface normals/absolute difference provided the best alignment results, performing well both if shape changes were localized and if they were globally distributed. Mean alignment errors for this method were less than 0.285 mm for each of the three translation directions and less than 0.357° for each of the three rotation directions. This algorithm could be helpful to patients, prosthetists, and researchers developing treatments to overcome the detrimental fitting effects of residual limb shape change.