In this study, we propose two algorithms for measuring the distance between shape boundaries. In the algorithms, shape boundary is represented by the Beam Angle Statistics (BAS), which maps 2-D shape information into a set of 1-D functions. Firstly, we adopt Dynamic Time Warping method to develop an efficient distance calculation scheme, which is consistent with the human visual system in perceiving shape similarity. Since the starting point of the representations may differ in shapes, the best correspondence of items is found by shifting one of the feature vectors. Secondly, we propose an approximate solution, which utilizes the cyclic nature of the shape boundary and eliminates the shifting operation. The proposed method measures the distance between the features approximately and decreases the time complexity substantially. The experiments performed on MPEG-7 Shape database show that both algorithms using BAS features outperform all the available methods in the literature.