This paper investigates the spectrum of MHD waves associated with plasma sheet configurations and applies the results to the plasma sheet in the Earth's magnetotail. We represent the plasma sheet by an inhomogeneous continuous one-dimensional static equilibrium model (Harris sheet) and discuss its response to small perturbations in the framework of ideal MHD theory including compressibility. The wave frequency is calculated from a generalized singular eigenvalue problem which in general contains a continuous spectrum with eigensolutions becoming singular at frequency-dependent positions from the neutral sheet. The singular modes lead to time-asymptoically damped solutions for the physical perturbations by the process of phase mixing. In the special case of two-dimensional perturbations, the spectrum displays discrete eigenfrequencies with smooth eigensolutions in addition to a continuous part. The application of the theory to the Earth's magnetotail on the basis of the hypothesis that observed waves in the plasma sheet belong to the undamped part of the spectrum leads to the result that the lowest two-dimensional modes are natural candidates for the observed oscillations with periods of the order of minutes. The lowest eigenmode of the discrete spectrum has an antisymmetric wavy structure and is consistent with the mentioned periods if the wavelength along the tail is of the the order of the plasma sheet thickness. ¿American Geophysical Union 1990