Summary: Analytical solutions for natural frequencies and mode shapes of elliptical cylindrical acoustic cavities were obtained by solving the homogeneous wave equation in elliptical cylindrical co-ordinates. Both hollow cylinder and annular cylinder cases were considered. The characteristic equation was obtained in terms of Mathieu functions. Natural frequencies and mode shapes were calculated for cavities of the size used as a typical hermetic compressor shell or a small automotive muffler. The results were compared with those of circular cylindrical cavities which have the same cross-sectional area and volume. The influence of the eccentricity on the general characteristics of cylindrically shaped acoustic devices is discussed.