High-resolution observations suggest that quiescent solar prominences are made of small-scale fibrils stacked one after another in both the vertical and horizontal directions. These fibrils are interpreted as the cool, highermost part of much larger coronal loops which are rooted in the solar photosphere. On the other hand, there is some evidence showing that small amplitude oscillations in prominences can affect individual or groups of fibrils, which vibrate with their own periods. Using a simple magnetostatic model to represent the fibril structure of quiescent solar prominences, Joarder et al. (cite{joarder}) investigated some oscillatory properties of the Alfvén and fast magnetohydrodynamic modes. In this paper, with a proper treatment of boundary conditions, we reexamine their configuration and explore more deeply the basic features (mainly frequency and spatial structure) of the fast mode. The main conclusion is that, for reasonable values of the fibril's width, perturbations extend far away from its axis and, therefore, a single oscillating fibril can excite oscillations in neighbouring ones.