This paper presents a mathematical model of the traditional musical instrument, the kompang. In this study, a mathematical model of the kompang membrane is developed to simulate the vibration of the kompang membrane in polar coordinates by implementing the Fourier-Bessel wave function. The wave equation in polar direction is applied to provide the vibration modes of the membrane with the corresponding natural frequencies of the circular membrane. The initial and boundary conditions are determined to allow the development of numerical equation based on kompang membrane attachment. The mathematical model is coded in Smath for the numerical analysis as well as the plotting tool. Two kompang membrane cases with different membrane materials i.e. goat-skin and x-ray film are tried to test the model. The Finite Element Method (FEM) programme, Mecway, shows that the natural frequencies and the corresponding mode shapes are comparable with those from the developed model.