Low-frequency pressure and magnetic oscillations observed by Cluster in the plasma sheet are investigated with the aim of determining if they are magnetohydrodynamic (MHD) eigenmodes. We analyze the plasma sheet crossing occurring on 22 August 2001, as the magnetosphere was first quiet and then active, and compare the observations with theoretical results concerning the MHD propagation in a Harris sheet. The theory shows that the eigenmodes have periods scaled by a characteristic time, τ, equal to the ratio between (1) the thickness of the sheet and (2) the sound speed. Using the Cluster 4 spacecraft, we estimate the sheet thickness and determine this characteristic time. It is compared with the typical periods of the fluctuations deduced from a wavelet analysis. During the quiet period, the fluctuations have periods larger than 100 s or 15τ. Discrete MHD eigenmodes with such periods would have wavelengths larger than the distance separating Cluster from Earth (18 RE). Thus they are very unlikely interpreted as freely propagating eigenmodes. However, fluctuations of shorter periods (∼20 s) are observed during and just after the substorm onset. We demonstrate that they are compatible with the fundamental MHD eigenmode (kink-like mode) of the sheet, with a wavelength of ∼5–6 RE, their direction of propagation being not determined at this stage of the analysis. We thus conclude that freely propagating MHD eigenmodes observable by Cluster would have periods that hardly exceed a minute for typical plasma sheet parameters (thickness of 1 RE, temperature of a few keV).