The normal modes of vibration of a gaseous medium in a parabolical cavity are investigated. The wave equation in parabolical coordinates is solved formally for the most general case in terms of Bessel wavefunctions. The first ten terms of the Bessel wavefunction of order 0, 1, and 2 are computed for arbitrary arguments. As the analytical solution of the wave equation for a cylindrical cavity has been used for computing the frequencies of the standing waves tn the combustion chamber of a liquid‐propellant rocket motor, the present analysis may be of value to the development of a rocket motor of more general form.