Observations of quiescent filaments show very fine structures suggesting that they can be composed by smallscale threads or fibrils and, on the other hand, twodimensional, high-resolution observations have pointed out that individual fibrils or groups of fibrils may oscillate independently with their own periods. Using Cartesian geometry, Díaz et al. (2001) studied the fast magnetohydrodynamic oscillations of a single and isolated prominence fibril showing that for reasonable values of the fibril's width the perturbations extend far away from its axis. This study can be looked at as incomplete since, by considering only one fibril, the interaction between the different fibrils composing the prominence was not taken into account. In this work, we study the fast MHD modes of oscillation of homogeneous and inhomogeneous multifibril Cartesian systems trying to represent the oscillations of the fibril structure of a real prominence. In the case of an homogeneous multifibril system, our results show that, for a realistic separation between fibrils, the only surviving mode is the symmetric one, which means that, at the end, all the fibrils oscillate in spatial phase with the same frequency. An inhomogeneous multifibril system can be obtained by varying the Alfvén velocity within each considered fibril, and the results show that there are not symmetric or antisymmetric modes, that the amplitudes of oscillation are higher in the more dense fibrils, that the frequency of oscillation of the fibrils, due to the only non-leaky mode, is slightly smaller than that of the dominant fibril considered alone, and that all the fibrils oscillate in phase. Finally, the introduction of a wavenumber results in a better confinement, a lower interaction between fibrils and a decrease in frequencies.