The analysis of the shape of calcified structures is known to be particularly relevant to address species identification and stock discrimination. Previous work mainly relied on Fourier shape descriptors, which achieve a global characterization of shape. In contrast, we investigate the potential of shape geodesics which rely on local shape features for classification issues. Classification performances are reported for several real datasets of calcified structures. The proposed shape geodesics scheme is shown to significantly outperform the standard Fourier approaches.