Fast retrieval using organ shapes is crucial in medical image databases since shape is a clinically prominent feature. In this paper, we propose that 2-D shapes in medical image databases can be indexed by embedding them into a vector space and using efficient vector space indexing. An optimal shape space embedding is proposed for this purpose. Experimental results of indexing vertebral shapes in the NHANES II database are presented. The results show that vector space indexing following embedding gives superior performance than metric indexing.