This paper presents a novel shape representation, called elliptical shape coding, and uses it to develop an efficient shape retrieval algorithm. The elliptical shape coding transforms an original shape, which is a single, closed contour in our experiments, into a periodic signal. The alignment between two shapes is accomplished efficiently by performing convolution of the corresponding periodic signals. Unlike previous approaches, we taking advantage of a priori knowledge hidden in the shape structure to produce shape matches with a significantly lower computational cost. Experimental results on an MPEG-7 shape database demonstrate the effectiveness of the proposed method.