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We propose a shape descriptor based on the differential entropy of multiscale curvature (MEC), which has a better shape discrimination ability than the normalised multiscale bending energy (NMBE) descriptor. We compare both NMBE and MEC with a monoscale descriptor by conducting multiple-class classification experiments on images from three public datasets: Kimia99 (99 shapes/9 classes), MPEG7-CE (1400 shapes/70 classes) and Flavia leaves (1907 shapes/32 classes). The classification results for precision, recall and F1-score measures, show that the use of MEC improved shape description for the MPEG7-CE and Flavia datasets. A qualitative analysis based on visualisation of pairwise Euclidean distance matrices also confirmed that MEC is a competitive method of shape description compared to NMBE for these datasets.