The frequencies of the lower modes of vibration of the Indian drums, the right‐ and left‐hand thabalas which have circular drumheads loaded concentrically in the former and eccentrically in the latter have been computed by the method of variation of parameters incorporating the variation of the surface density of the drumheads in the normalizing integral. The boundary value problem is first formulated in terms of a modified form of bipolar coordinates suitable for the eccentrically loaded left‐hand thabala, the boundary value problem of the right‐hand thabala being obtained as a special case when the eccentricity parameter vanishes. It is then shown that the harmonic character of the modes of vibration is primarily determined by the ratio of the radii of the loaded and unloaded regions, the eccentric placement of the loaded region in the left‐hand thabala merely bringing about a small separation between the frequencies of the even and odd modes.The computed frequencies are compared with previous calculations. In the case of the right‐hand thabala where exact values are known the agreement is as good as 1% and in the case of the left‐hand thabala where only approximate values are known the agreement is about 10%.