Measured back surface topographies can be useful to monitor the external manifestation of scoliosis to avoid exposure to large doses of radiation. Manual shape fitting of back surface topographies from successive clinical visits can then be used to detect differences. Automated matching of the measured topographies has been seen as a possible improvement on manual comparisons. Recognizing that two changed surface cannot be expected to be simple rigid replicas of each other, the goal of this research has been to develop a new algorithm based on a non-rigid surface matching algorithm, suited to matching the surfaces into same reference frame while also estimating the parameters of the scoliosis deformities, and eliminating noise due to normal body change caused by growth. Back surface topography data from laser optical scanning have been automatically matched by a least squares non-rigid matching algorithm. The algorithm includes new parameters able to model shape changes caused by normal growth and scoliosis deformation. This non-rigid matching algorithm returned r.m.s. values for surface closeness which were improved by at least 10% over rigid matching. Experiments on various scoliosis data demonstrate that the non-rigid matching algorithm is able to accurately match the surfaces while simultaneously extracting parameters representing patient shape change. The non-rigid algorithm has proven to be an improvement on the classical rigid surface matching approach which allows positional fit rather than shape fit. Measured back surface topographies can be closely matched to monitor the external manifestation of scoliosis.