Abstract: In this paper, we take the Chinese chime bell as a truncated elliptical cone. The fle-xural vibration of an elliptical cone is analysed for the fundamental modes of vibration of chime bells The approximate expression of frequency for the two tones of a chime bell takes the form:f=K\sqrt \fracE3p(1-\sigma ^2 \rm \times \fractb^2 where t is the bell thickness, b is the long axis of elliptical cone base and factor K is a function of the bell shape parameters. This expression shows the influence of bell shape and size upon the frequencies. From the frequency relations of the two fundamental tones we can suggest in detail the method of tuning used in ancient times. As an example, the relations between tone frequencies and bell size are studied for a group of ancient chime bells.